To achieve this i think you need to solidify the HRE and from their you could proceed to the eastward expansion so the perfect situation is with Henry VI of the HRE
The first 4 points are what happened :
1. Captures and ransoms Richard the lion heart (he now has massive money resources)
2. Captures Sicily (adds to his personal lands so now is the richest person in western Europe)
3. Negotiates with the ERE and gets funds :::: also opens the opportunity to combine the ERE and WRE ( Upon the deposition of Emperor Isaac II Angelos Henry openly threatened with an attack on Byzantine territory. 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 chronicler Niketas Choniates his legates were able to collect a large tribute from Isaac's brother and successor Alexios III, which, however, was not paid before Henry's death. .......https://en.wikipedia.org/wiki/Henry_VI,_Holy_Roman_Emperor)
4. IN 1195 he starts work in Germany for a crusade : and negotiates with the German nobles for a Hereditary Monarchy ( His next aim was to make the imperial crown hereditary. Henry tried to secure the Imperial election of his son Frederick II as King of the Romans, which however met with objections raised by Archbishop Adolf of Cologne. Spending the winter in Hagenau Castle, the emperor and his ministeriales evolved the idea of a hereditary monarchy. Though they would have lost their right to elect the kings, the secular princes themselves wished to make their Imperial fiefs hereditary and to be inheritable by the female line as well, and Henry agreed to consider these demands. The emperor also bought the support of ecclesiastical princes by announcing that he would be willing to give up the Jus Spolii and the right to receive recurring earnings from church lands during a period of sede vacante. At the Diet of Würzburg, held in March/April 1196, he managed to convince the majority of the princes to vote for his proposal. However, Archbishop Adolf of Cologne did not even put in an appearance and several princes, predominantly in Saxony and Thuringia, were still dissatisfied. ...( https://en.wikipedia.org/wiki/Henry_VI,_Holy_Roman_Emperor)
5. He died at 28 in Italy shortly after this. So here is where you vary it:::::
a. He gets agreement in 1197 for hereditary monarchy.
b. Does a successful crusade to the holy land with a large German + allied army. (btw butterfly's 1204) The marriage takes place between Byz princess and Philip (Henry's brother)
c. With the prestige of a successful crusade (Saladin dead at this time and the Arab states in chaos -- and Barbarossa army had easily defeated the Turks so i see good chance of success) and the wealth captured he would have massive resources and prob put one of his brothers on the crown of the K of Jerusalem. The theory which was popular at the crusader times was to capture Egypt (so if he did then even more wealth and a well financed crusader state)
6. So we have a 30 year old emperor who was aligned (blood marriage) with the ERE, owned southern Italy, had created a hereditary monarchy and a centralized HRE government. Natural expansion would have been east. So as the most powerful emperor / king in the world a natural crusading focus would have been into Prussia and Lithuania. But instead of the Teutonic knights (which Henry VI supported in Sicily) you would have a united WRE with massive resources conquering east.
a. 1205 - 1215 conquest of Prussia and Lithuania
b. 1215 - 1225 conquest of Novograd
c. 1225 - 1235 conquest of Poland
Why is it it's always you who comes with such epic TL ideas but then nobody uses them.