Honestly I think that the King Tiger should only be able to be called in if all 3 trucks are set up at once.
It seems cheesy how you can make a great effort to kill a truck then he just calls in the King Tiger anyway at no great inconvinience.
Other than that the King Tiger is fine.
If you want like that you need to buff stats or make it cost less
The reduced vet solution isn't a bad idea but it would mean creating specialized game rules for one specific unit that aren't in any way clear to the average player. I'd much rather see the churchill just brought in line with the survivability of every other heavy tank.
And 1 only on the field like every other heavy tank