In the way of preparing a TL about the creation and expansion of a Teutonic Empire, I want to check with you the plausibility of some of its chronological milestones (not definitive though, just for brainstorm).
The basic ideas are these:
* 14th century: PoD when the Monastic state of the Teutonic Knights (TK) develops into a dynastic one, based on Prussia (Malbork) but also controlling the Baltic duchies. Samogitia is transformed into a duchy and some dynastic union with Poland is agreed or somehow forced.
* 15th century: first expansions of the Teutonic Kingdom, mostly to Southern Poland, Lithuania propria and the area of Pskov. In the second half of the century, the TK is increasinlgly centralized and expands into HRE through Brandenburg. The relationship with the Papacy becomes more and more tense, because the Popes of the moment supports the HRE and the TK is trying to challenge its power. By 1500, the TK is considered a major rival by the HR Emperor and Austria.
* From 1510 to 1540: the Reformation is well received by TK. The TK is upgraded to Teutonic Empire and its won National Church is created, with 'holy see' in Marienburg (Malbork). This move is contested by Austria, but Ottomans then sieges Vienna; Teutons and Ottomans sandwich the Austrians and they are finally crushed: the Teutons acquire the Austrian territories in the north side of the Danube while Ottomans make their way into Italy, occupying Rome (= war with France and Spain). The Teutonic Empire takes advantages of the chaos and acquire new territories of the HRE that support Reformation, like some of the Swiss cantons and the Northern states.
* From 1540 to 1572: Ottomans hold Rome and the Catholic powers ally against them. The quick expansion of the Teutonic Empire creates internal divisions and the current dinasty is dethroned. A new dinasty takes control of the Empire, which is further centralized.
* From 1572 to 1620: Ottomans are finally expelled from Italy and start to decline. The Teutons takes control of some of their former territories in Northern Italy and pushed the border with the Ottomans southwards, establishing a stable one in the Save river. Reformation succeeds more than OTL and Catholics are reduced to Spain, Italy, France and some Western German states plus Bavaria.
* From 1620 to 1660: Once Ottomans are defeated, France and its German allies (Catholic German states) declares war to the Teutons. After a couple of decades of war, the HRE is finally abolished: the Teutons acquire all the German lands east of the Rhine, excepting Baden, Württemberg and Bavaria, remaining as puppet states. France holds the Rheinland, Belgium and part of OTL Switzerland. Spain holds all Italy south of the Po; the rest of Northern Italy becomes Teuton, excepting Savoy.
* From 1660 to 1720: Denmark and Sweden, former Teutonic allies, declare war to the Teutonic Empire, after the 'illegal' annexation of Pomerania in 1665. The Teutons occupy Jutland in 1670, and the Danish king retreats to Norway; the Danish islands are occupied some time later.
Sweden manages to avoid defeat, but cedes Ingria and part of Karelia to the Teutons for signing peace.
* From 1720 to 1790: the Teutonic Empire pushed the Ottomans out of Ukraine and the Empire reaches the Black Sea. The Teutons divide Ukraine with Russia, in order to establish peace with them and a stable border from the Ladoga until the Black Sea (peace of Lemberg in 1772). The political capital is relocated to Vienna in 1781, but Marienburg remains as the religious center.
* From 1790 to 1820: the French Revolution causes a war with the Teutonic Empire. Some anti-revolutionary regions embrace the 'Teutonic help' but they are finally invaded. After decades of war, a peace in 1820 establishes a new border: France loses all territories east to the Rhone and north to the Somme. The Teutons also annexes the remaining German states and Savoy. Italy is granted with independence from Spain.
* From 1820 to 1870: the Teutons acquire its lasts territories in the Balkans, pushing Ottomans out of them in a series of wars. An independent big Greece is created, but the rest of the Balkans (north to Macedonia) is annexed by the Teutons. This area is heavily resettled with Germans.
* From 1870 to 1905: a Liberal revolution in 1875 puts an end to the conservative empire. A new Constitution is written in 1878 and a Parliament established in Vienna. The Empire is rationally divided in hundreds of 'Kreise', that also freely groups in länder, with some degree of autonomy and own parliament.
* From 1905 to 1930: a coup puts an end to the constitutional monarchy, establishing a pseudo-fascist one. Many non-German people is pushed out of the Empire and political parties are banned. The constitutional monarchy is recovered in 1930 after a pacicifc revolution.
* Since 1930: the Empire boosts a European League of Nations to re-establish peace and good relations with France, Spain, UK, Italy, Greece, Norway and Sweden. Russia remains as a 'natural' rival power.