Color me skeptical about that. My understanding of Ivan the Terrible is that a lot of his later reign was strained by the Livonian War which lasted 25 years, which saw things like the Oprichnina, and Sack of Novgorod happen. I would say you cannot have a shorter Livonian War that somehow magically sees Ivan the Terribles reign play out the exact same way. While I would argue that Ivan certainly had a high opinion of himself, I feel that him killing his son, or even just being left with Feodor are not done deals that are somehow not impacted by the Livonian War.
An idea that Ivan was a nice and meek person and that only a prolonged war turned him into a monster is, of course, quite interesting but, unfortunately, it belongs to the same category as him being forced to cruelty by the evil plotting boyars (see Eisenstein's movie). Ivan started killing people for fun or revenge when he still was a teenager, well before the Livonian War. Conquest of Kazan was not gently done either, and the list is going on. Shorter Livonian war would change the details but not a principle.
As far as Oprichnina is involved, it was explained long ago that
formally creating a separate "state within state" was the only way for him to bypass the restrictions of the existing system: he could execute whoever he wanted but he could not make an administrative or military appointment that would violate existing system of "mestnichestvo". However, within this new "state" the rules did not apply and he could make military appointments at will (oprichnina, among other things, was an army). Implementing this idea as OTL monstrosity was a byproduct of his personality.
The real reasons behind Sack of Novgorod are unknown and there was more than one theory on the subject out of which the evil plot of the Novgorodian elite with a purpose to switch to Lithuuania is only one. Not too convincing one, to be sure, taking into an account that traditional Novgorodian aristocracy mostly was not there after the wars with Ivan III which ended up with "repopulating" the area with the loyalists from Moscow. Even if one assumes that there were few high-placed turncoats in Novgorod itself, this can't explain genocide conducted in the whole region.
The whole story about murder of Ivan Jr. seems to be put to doubt recently but, while by changing something we can't guarantee that the rest will be exactly the same, there is no reason to insist that these events would not happen. The same goes for your conclusion that everything, including an alleged murder of his elder son, did happen exclusively due to the Livonian War.
As for this part, I would say Russia suffered less from "Backwardness" from and more political disruption from the later parts of Ivan the Terrible's reign with The Oprichnina, Time of Troubles, and the invasions and political disputes that came along with it, as well as hostile neighbors.
Let's start from the beginning. Russia was backward. Ivan III, grandfather of Ivan IV, had to invite the Italian architects to build the big cathedrals because Russians at that time simply did not know how to do anything of the kind (so-called "st. Basil Cathedral" built by Ivan IV has exotic exterior but there are no big spaces inside). The same goes for the fortifications of the Kremlin. Ivan IV
knew that Russian military system is lagging behind the West and his initial military reforms involved both copying and direct hiring. Venetian ambassador was reporting in 1557 that Russian troops included "20,000 mounted shooters Saxon style and 30,000 infantry Swiss style" (while both the numbers and references look suspicious there is no reason to assume that they are a complete fantasy). Report by another visiting Italian says "... he also uses the foreign soldiers, mostly German infantrymen." Presumably, during the Livonian war Ivan had up to 7,000 Germans in his army and there are explicit references to the foreign troops left as garrison of Moscow in 1578 - 80. Russian army was definitely lagging behind in the area of a siegecraft, its artillery, while numerous, was not organized to be useful in the field battles, etc.
What's worth noticing is that in OTL Livonian War Ivan seemingly made a stress upon the "Asiatic" (well, Tatars were, of course, Europeans) style of a warfare at the expense of further development of the "Western" style troops. Streltsy never were developed up to the contemporary Western infantry standards (IMO, by their tactics they had been closer to the Janissary in the terms of almost exclusively relying upon firepower) and, whatever were the initial attempts in the area of a cavalry, it seems that the Tatar contingents and the traditional feudal militia had been prevailing. While there were definitely some foreigners serving in Oprichnina, it does not look like its military organization was advanced (all the way to the contemporary descriptions implying that they were armed with the bows).
Of course, events as disastrous as ToT were huge disruptive factor but "hostile neighbors", including successful Polish intervention during the ToT, became a serious issue due to the Russian military backwardness. Even few decades after the ToT, with a considerable work already done on modernization of the Russian army (including massive hiring of the foreigners), Smolensk War had been lost because of that weakness.
Then, of course, goes an issue of a general economic development in which Tsardom was clearly behind the West in the terms of manufacturing the goods and even the trade perceptions. In OTL the government (and Orthodox Church) were severely travels abroad as dangerous for the soul so how isolationism could not result in a backwardness?
Having a window to west means nothing if the rest of the house is on fire, and believe a shorter victorious Livonian War can potentially remove all those problems that plagued Russia.
That's the whole point! The argument about absence of the "window" as the main factor had been repeatedly used by the historians, both Russian and foreign, for almost 3 centuries. Of course, the part about "house on fire" is neither here nor there because Russia was noticeably lagging behind the West at least couple generations prior to Ivan IV and kept lagging for at least a century after that "fire" was extinguished (if, rather optimistically, we assume that this ceased to be the case during the reign of Peter I).
But would the earlier functioning outlet produce a noticeable change in the situation?
However, more to the point, keeping Narva and how successful it would be, depends on what happens internally as well. If Novgorod is still devastated by Ivan the Terrible then perhaps could be become an important city to take Novgorod's place. However, if Novgorod is not devastated Narva could serve by being a port of entry near such an important city, but not fully eclipsing the city.
By the time of Ivan IV Novgorod lost most of its trading clout thanks to the efforts of Ivan's grandfather who mostly destroyed its merchant class and limited contacts with the Hanseatic League. Ivan IV continued work in that direction but did not completely kill importance of the city due to the obvious geographic reasons: almost inevitably it was on a traditional route to the Baltic coast. What Novgorod
was in OTL after the dust settled, was a transit city through which the goods were coming to and from Narva, a Swedish port officially designated as a major outlet for the Russian trade. If Narva remains Russian all the time then, one way or another, Novgorod would remain important in a capacity close to one of OTL.
However, the important question is would this scenario be enough for Russia in a long term? The main problem with Narva as a port is that it was very convenient for the trade via Pskov (which was relatively peripheral city) but not too much so for Novgorod. While in OTL Peter started GNW with an attack on Narva, soon enough he switched stress to the North: route Ladoga Lake - Neva River - Gulf of Finland which was better oriented toward the Central Russia (and was a part of the old Novgorodian trade route).
@Valena argued that a new outlet in Neva mouth would be almost inevitable for a growing trade volume.
