What's making it so hard to get JP4 or a StuG?
Well if you absolutely rush a stug and skip T1 and T2 buildings then 70 (teching -starting fuel)+90+75=235 fuel.
In order to get a centaur you only need 10+110+100=220 fuel.
So while your opponent still gets a centaur before your rushed stug all you have is pioneers and mgs, maybe osttruppen
It is easier to rush a JPIV but I wouldn't say a JPIV is effective on all maps.