As you have noticed, nobody is going to support such a rework in this "l2p" community where everything is the player's fault and totally not a design oversight.
Even if a change makes sense it will not be even considered the slightest.
Medical, Pepair and KT unlock. The first 2 are the generic ones already featured in the other HQ trucks.
The KT unlock is the same as the Panzer Elite Panther combat group call in upgrade, you get it after all 3 HQ trucks are setup, serves as an additional tech-ing so people don't bitch that it's wayyy to cheap to get such an "OP" unit as the KT.
MG34 is buffed and becomes T0, raketen is replaced with a PaK 38/40, but seeing as Relic won't bother with a new model it's going to have to be a Pak 40, requires either additional HQ truck to unlock such as the MG34 right now.
Schwerer Panzer HQ gets an unlock upgrade for it's Flak 40 gun however, you gain the ability to manually aim it or some sort of other buff.
OKW either loses the ability to salvage entirely or the ability is only to gain ammunition, but gains access to resource caches, balances it out so you can't shorten the time to get a KT so much as suggested by AElegion.
M7 105 mm Howitzer Motor Carriage
This is different than the M7B1 Priest for this is a direct fire support unit and is historically accurate. Or at least accurate enough for CoH2. The unit should preform similarly of a combination of a SU 76 and the Brumbar. It has good anti-infantry while still able to damage medium tanks with at least direct hits.
The main gun is similar to the Brumbar except for the following.
-Range is increased to 55 from 40
-Unable to fire on the move
The MG damage is equal to the M20 to provide additional fire support
The armor is the same as the priest (60) but the health is increased to 400 from 320 for increase resilience.
I really like this.
If memory recalls correctly there is something similar in Wikinger if you've ever played that, Assault guns can fire both directly and indirectly since they're armed with howitzers (or field guns in the case of the SU-76).
And I've never understood why proper Self-Propelled Guns such as the M7, Sexton, Hummel, Grille and Wespe (just to clarify, Sexton in this game as well as CoH mods, and the Grille and Wespe from CoH's mods as well) cannot fire directly, they all have their guns pointed flat forward but none of them had the ability to do so, and it's possible since it's done with the Assault guns.
Now one argument could be that they would become OP, but I don't really consider a glass cannon on tracks with a short direct fire range to be OP by an margin, if you want a proper assault vehicle you will call in something more armored. Direct fire these vehicles should be used ONLY if needed, in a situation where the vehicles are moved forward to gain more range and let's say an enemy infantry unit swoops in from somewhere, why couldn't they lob off a round before retreating to prevent the infantry unit from catching up to them so easily and save their skins? It just never made sense to me at least.
I do believe that all Armies should have an HQ medical upgrade like in Wikinger, not just the Soviets and OKW, but that may be just me.
As far as other things go, if it was up to me I'd replace the bugged raketen with a less gimicky AT gun and just give the OKW a PaK 40 at Tier 1, making the MG34 Tier 0 and buffing it a bit as to not still be the shittiest MG on the list.
Other balance changes to the OKW would probably be an upgrade to unlock the King Tiger, similar to the Panzer Elite's Panther battlegroup unlock from CoH, or straight up just put it in a another doctrine and give the OKW resource caches. I'd also suggest the same thing for the Raketen, make it a German M42 and stick it in a doctrine somewhere for when you wanna use it for shits and giggles.
As for the Brits, your light artillery mortar pit is a good idea as I've said before, but I still think that Planet Smasher's idea is superior due to it being mobile.
But if you really want to give the British player another option you can probably include your light artillery pit idea as well for like let's say the Advanced Emplacements Regiment to give it more of a unique feel or something.
Because I really do love your idea, but I just prefer a mobile mortar, that's all.
Edit: I forgot one more thing, maybe an upgrade for the heavy Panzer HQ truck for the OKW to unlock it's gun? It's been suggested quiet a while now. Perhaps with it and my suggested unlock for the KT it would suffice as to allow the OKW to construct resource caches?
I also forgot if I've asked you this before but... Can you make your light artillery pit to be garrisonable similar to what Planet Smasher has done? So let's say you can garrison it with MGs and mortars, perhaps even a light AT gun and not just infantry units?