Well, the thing about Belgrade winding up in AH's armpit - it was sort of already there, especially after 1908.
As far as "access to the sea for Serbia"... even Wilson trotted this one out in the 14 Points. Again, whose territory were they going to steal for said "access to the sea"? They had attempted it with northern Albania, despite the dearth of ethnic Serbs there or in Kosovo for that matter. The taking of Vardar Macedonia was itself just part of a grand southward thrust with the intent of taking Thessaloniki... again, no Serbs anywhere in the vicinity. The only "logical" outlet would be Kotor, which had been an old Venetian port... and getting Kotor would depend upon union with Montenegro (which, incidentally, required a bit of bullying and cajoling after WWI to make that happen - after all, the Montenegrins had been more or less independent for what, 500 years?). The Bribe er I mean Treaty of London even promised Serbia some Adriatic coastline north of Kotor... all Croat and all Catholic AFAIK.
The thing is, it was about sea access that wasn't dependent upon Austria (and preferably on the Adriatic). That was Serbia's goal after that thug Apis murdered Alexander and a different dynasty came to the throne. Austria (understandably) preferred the old situation whereby Serbia depended on Austria's ports. However Austria's attempts to deny Serbia independent access to the sea began to colour a lot of their interactions with Serbia and over time, even after Serbia (and Montenegro) began to exhibit rudimentary constitutional democracy in the early 1900s and the political parties that came to power through voting did have it as their goal to gain access to ports that didn't depend on Austria. Hence in 1905 Serbia and Bulgaria entered a customs union *so Serbia would have access to Bulgarian ports tariff free), to which the Austrian response was a tariff war on pork from 1906 to 1908. Then in 1908 Austria annexed Bosnia, which Serbia had designs on (including as a possible access point to the Adriatic, besides its population of Serbs and other South Slavs) which sparked the Bosnian Crisis. Serbia backed down from protesting that move and then looked at conquering Ottoman lands to their south to gain sea access via Albania (besides wanting to conquering what was sometimes called Old Serbia that included lands inhabited by Serbs as well as non-Serbs). Austria didn't like this possibility and pushed for an independent Albania (which was a definite good move in and of itself by Austria as having Albania partitioned between Montenegro, Serbia and Greece would have just been awful for the Albanians given that they deserved their own independence just like any other Balkan peoples and that they ended up being subject to the independent Balkan States, especially Serbia I believe, treating them terribly during the First Balkan War and aftermath). So now with Albania closed off and relations souring between Bulgaria and Serbia, Serbia opted to keep parts of Vardar Macedonia it had previously agreed would have gone to Bulgaria, earning the latter's enmity. While Pasic had wanted Field Marshal Putnik to go for Thessaloniki during the first Balkan War, Putnik apparently opted instead to head into Albania and leave the race for Thessaloniki (with the area of what is now Greek Macedonia being a mix of Greeks, Slavs, Turks, Aromanians, etc) to Bulgaria and Greece. Then we get the Second Balkan War and the borders settle down into what we are familiar with for 1913-1914. At this point Serbia's aims for an Adriatic port seemed to have followed 3 parallel tracks:
1. Gain influence or control over Albania or at least northern Albania (that wasn't really going anywhere except that Serbia managed to make temporary allies with local Albanians in the north who might have held a grievance against other groups of Albanians in the north or against the central government)
2. Pursue unification with Bosnia, including supporting Bosnian Serbs that pushed for independence (sometimes violently) from the Habsburgs and union with Serbia
3. Pursue unification with Montenegro. This was actually progressing in 1914 as Serbia and Montenegro were negotiating a union that would involve a customs union (and so free access for Serbia to the Adriatic via Montenegro). Ultimate unification with Montenegro required cajoling and bullying against the Montenegrin
King (who only wanted unification if he became King of the unified state) rather than cajoling and bullying Montenegro generally since one of the leading parties that played a key role in the unification in 1918/1919 (via the Podgorica Assembly rather than the National Assembly) was the pro-unification People's Party which had won majorities to the National Assembly in the free elections of 1906 and 1914 . In the 1914 elections the People's Party gain an absolute majority of the elected seats (25 of the 48 elected seats) against the King's favoured True People's Party (TPP) and they (the People's Party) formed a coalition with a "Unified Serb Youth" party (that had won 2 seats) and group of former TPP members that had won 17 seats. The TPP itself meanwhile had previously been governing since the 1907 election when the People's Party boycotted it over the then Prince's poor relations with Serbia and what they claimed was his hostility to the party. The TPP was then apparently made the only legal party shortly after and naturally won the 1911 elections (though some People's Party members won seats as independents) and then went from having 53 seats in 1911 to only winning 4 seats in 1914 when multiparty elections were allowed again. In fact, since the formation of Montenegro's Assembly in 1905, the pro-unification People's Party won the majority of elected seats in both 1906 (51 of 62 elected seats; there were also 14 appointed seats) and 1914 and only didn't win majorities when they boycotted (1907) or were banned (1911).
Had World War I not happened, it seems likely that Serbia would have entered into at the very least a strong confederation with Montenegro and gained access to the sea via that confederal customs union.
EDIT: Now this is a bit of a tangent to the thread itself, but I've begun to wonder if a better approach by Austria-Hungary following the end of the pro-Austrian Obrenovic dynasty wasn't to recognize that:
1. the dynasty was likely going to end anyway - Alexander was 27 in 1903, his wife Draga was likely infertile and he seemed skilled at making enemies of everybody including his father and mother (over his marriage), his generals (over his marriage), his ministers (over his marriage), quite a few common folk (over abandoning his father's liberal constitution and resorting to the more conservative 1869 one until he finally gave way to some pressure and put in place a somewhat more liberal constitution in 1901) - even if he wasn't assassinated, chances are there would have been a revolution that overthrew his dynasty before his natural death. Alexander had already agreed that if his marriage with Draga produced no children that Prince Mirko of Montenegro (son of King Nicholas of Montenegro) would be declared heir. Alexanders most recent ancestors lived to ages ranging from 32 (grandfather), 47 (father) and 66 (great-grandfather). Let's say that he lives to be 56 and dies in 1932. At that point Danilo, elder son of Nicholas, is already King of Montenegro since 1921 and Mirko becomes King of Serbia. Just 7 years later Mirko becomes King of both Serbia and Montenegro. Apparently Mirko sympathized (or had even joined) Black Hand in 1911 (and in the immediate aftermath of the 1903 coup one of the coup plotters had suggested him for King of Serbia while some others advocated for a republic), so King Mirko of Serbia and Montenegro might not
exactly be the kind of ruler they would get along with.
2. you catch more flies with honey than with vinegar. So instead of annexing Bosnia and Herzegovina in 1908, perhaps they could have turned it into a new Kingdom of Bosnia as a kind of model Obrenovic-esque Serbia? In 1908 they could have set up a Kingdom of Bosnia with perhaps:
A. Prince Mirko of Montenegro (then aged 29) as King (which would almost surely have met with approval from Prince Nicholas of Montenegro and helped with Austrian efforts to pull Montenegro (or at least its leadership) away from Serbia; though if Mirko really did sympathize with Black Hand, then this could lead down the road to the Kingdom of Bosnia agreeing to join even a Karađorđević Serbia, especially as Peter Karađorđević of Serbia was married to Mirko's elder sister Zorka)
B. Alexander Konstantinovic (then aged 60) as King. Alexander being a colonel and the son of Anka Obrenovic, he had to flee Serbia for Austria-Hungary after criticizing King Alexander's to Draga - which might mean Konstantinovic not being distinctly
unpopular among the general Serbian public. Only issue with this move is that Alexander Konstantinovic died in OTL in 1914 at the age of 66. He had a son, Vladimir whom it seems had become a captain and married an American woman in 1900 (later marrying a French woman when his first wife died and having a son by this second wife). If his son Vladimir doesn't take the Bosnian throne it then likely goes to.....Prince Mirko of Montenegro via his marriage to Alexander Konstantinovic's daughter, Natalija (or perhaps to their son Michael who was born in 1908)
While establishing a Bosnian Kingdom out of the occupied Ottoman Bosnia would likely still invite Serbian protests (besides protests by the other powers), Serbia would still likely back down and any intrigue against the Bosnian state would be directed against the Bosnian royalty as more immediate rivals more often than against the Austro-Hungarian monarchy. Besides which setting up an
independent (but Hapsburg-aligned) Serbo-Croatian kingdom in Bosnia would provide a powerful counternarrative to what had been happening since 1903 and right up to 1914.