i have few suggestion to your idea which i really like btw.
"Großdeutschland" was opieOP division in entire Wermacht. They acually had a lot of heavy stuff and they were bloody elite. So:
1. becouse that division was very experience i would add upgrade for infantry (pio, grens, pgrens) called "extra training" - something like german infantry already has: extra unique abilities for each type of infantry
2. To make the concept more unique i would suggest Panzerfuzzilier rather than assualt grens.
3. 250 sdkfz is 4th MP call in unit so should be replace with ammo ability.
I would prefer that Tiger to be more diffrent that ostheer version. So expect panzer tactician i would add a smoke shot like cromwell has, expect mg a panzer commander, and ambush camo ability (but cannot move). Generally idea is great.
GD also had Tigers as well, only a regiment had the honorary title of Panzerfusiliers, the rest were basically Panzergrenadiers so you idea of infantry training does sound good. GD was also known for it's leadership so perhaps an Artillery Officer would also fit the theme.
Alternatively the Panzerfusiliers could also come mounted in a 250.