SO here is the best TL i can think of :
1. Barbarossa wins over the Lombard's
2. Barb has a friendly support of the Popes
3. Barb has son Henry VI made HRE
4. On crusade he does not go for a swim -- (his army badly defeated the Turks in Anatolia) -- so he captures Aleppo (makes it a crusader kingdom - which makes the Crusader states very viable) -- and Jerusalem - giving him massive political power.
5. now 1 of 2 ways -- the first is he listens to Richard and campaigns in Egypt, captures it , and takes 20% of revenue (with Richard 20% ) the rest supports the Crusader states. IN addition their is a massive haul of booty that he takes back to Germany (allowing him Prestige and wealth to bribe/ force the Princes to make Henry a heriditory monarch (Henry was very close to forcing this thru with the money from Richards ransom and capture of Sicily). With the French abandoning a very successful crusade a German is made the new King of Jersu. (Barb son Fredrick VI. ) ---the other is Richard is captured so provides the funds as ransom / i love the first way.
6. Barb returns to Germany and between bribes and prestige make the HRE hereditary.
7. Barb dies
8. Henry invades Sicily 1194 and captures the country (hemming in the pope in from the north and south). He now is ruler of a united Germany, His brother is K of J under the Emperor, and Sicily (very rich) is directly his. The Lombard states in the north are also his (and with a lack of the traditional battles between the pope and the Emperors ) they stay as part of the HRE. (much of the wars were fought over the Emperor desire to appoint bishops in Germany).
9. IN 1195 -- He already evolved plans to betroth his younger brother Philip to Isaac's daughter Princess
Irene Angelina —deliberately or not— opening up a perspective to unite the Western and Eastern Empire under Hohenstaufen rule. According to the contemporary historian
Niketas Choniates his legates were able to collect
a large tribute from Isaac's brother and successor
Alexios III (
https://en.wikipedia.org/wiki/Henry_VI,_Holy_Roman_Emperor)
10. No 1204 4th crusade
11. So now u need to keep Henry alive (does not go hunting in Italy) -- and have him rule for 20 years more -- with the Emperor in alliance with England / Henry brother (potential emperor in Byz ) -- his other brother emp in KOJ -- and Sicily in his control -- plus an easier relationship with N Italy and the Pope . With a strong central gov .