I've got an idea:
We give OKW some sort of Heavy Pios. Let's call them Sturmpioniere, and give them a similar weapons profile like PGrens, for short- & mid ranged engagements, with lot's of DPS!
How does that sound?
Really not a huge fan of your idea, mainly because of the forced change in combat distance - a doctrinal upgrade might be a fun option to have though.
Early to mid game Sturms suffice, however lategame Sturms are on sweeping/repair duty pretty much full time. I agree on upgrade.
Off topic, pzgrens are okay because they're good at defending Osts support weapons and for flanks, two things the OKW lack.
@Katitof
Only dedicated anti-infantry squad of OKW are Obers. Pfusilier, falls, are utility units: JLI are *supposed* to be light force multiplier/recon but are currently OP, however their role is kept because Volks suck.