So, after 27th February update, I still think Teutons need some buff, so this is my idea, which is still similar to the first toppic of the post:
Take away crenellation, give castles +1range in caste age and +2 in imperial as a civ bonus, and ad a new imperial tech civ:
Deus Vult (600f 400g): infantry (included Teutonic knight) gains 5% speed for each relic (max 2 relics for barracks unit, max 4 relics for TK).
That would define Teutons as an infantry powerhouse and would make sense according to history