Luftwaffe Ground Troops: Luftwaffe support personnel like mechanics and supply troops who no longer had airplanes to support due to losses were often put into infantry units to support other ground forces.
Implementation: Add into a future doctrine or a doctrinal rework for Ostheer or OKW. Use the unit model of the Ostheer team weapon members from the PaK43 and Lefh howitzer. Armament would be Kar98ks and be a 5 or 6 man squad. It could be used to basically give OKW Ostruppen or to give Ostheer a unit kind of like Volksgrenadiers but can also repair, build sandbags, build Flak emplacements and lay barbed wire. Upgrades could be an LMG maybe an MG34 or MG42 or maybe two or three MP40s to provide a mixed weapon unit that can successfully defend a position, but is not very strong in the attack. OKW version could simply be identical to Ostruppen and added to the Luftwaffe doctrine, except have repair abilities. Ostheer version could be identical to Volksgrenadiers but no StG upgrade, no panzerfaust but have a repair ability and be able to construct Flak emplacements.
Of your 3 proposals, this is the one with the most merit. The other 2 aren't really needed but, the Ostheer Luftwaffe doctrines really do need to be reworked (possibly fused into one really good doctrine).
The new and improved version of an Ostheer Luftwaffe doctrine might look something like this:
0 CP Airdropped Medical Supplies (same as Luftwaffe Supply)*
1 CP Luftwaffe Ground Troops (pretty much what you've said above - essentially a Luftwaffe engineer unit)
3 CP Supply Drop Zone (same as Luftwaffe Supply and Close Air Support)
3 CP Fallschirmjaegers (basically the same as OKW version)
4 CP Luftwaffe Support Officer (much like the All-Units version, has all air support options available)
To my mind, this version would be much better than the 2 current Ostheer Luftwaffe doctrines, which are too munitions-intensive and provide no other units to supplement the core force. It also harks back to the CoH1 Luftwaffe doctrine, which was better than either of the current doctrines but contained units which are not available in CoH2.
I'd like to see this change happen during the next commander revamp (assuming there is another one).
[* If the Medical Supplies were incorporated as one of the Support Officer's abilities, the extra slot could be used to add the Pak43 (8 CP) to the roster (in place of the defunct Flak 88 from CoH1).]