The second MG34 only came out in the last moments of that match.
Your problem isn't enemy MGs, it's manpower bleed. Your first AT tool was a Bazooka Major, so his Luchs could bleed models from your squads pretty much uncontested for a long time. If your enemy fields a light vehicle like the Luchs you need field a response to it because it'll rule the battlefield until you do.
You also kept pushing Volksgrenadier squads in green cover with single Rifleman squads. Green cover halves received accuracy and damage taken, and movement reduces accuracy. This puts your Rifleman squads at a huge disadvantage when closing in, and the damage they take on the approach means they lose that fight and have to retreat. That costs you time, manpower and gains you nothing.
Push positions with more than one squad and ideally from more than one angle and you'll have more success displacing those green cover squads.
I don't know why they scrapped replacing ML-20 with B4 in the last patch. I mean nobody ever uses the vehicle direct fire ability unless they are trolling (usually) but at least it would make sense. Plus I hate abilities that are only available in one commander - IMO every ability should be in at least 2 commanders.
Mostly because the B4 is garbage. Otherwise yes, it'd be a good fit.
The reasoning behind putting the ML-20 in Tank Hunter was that the redesign is based around ambushing tanks: you use mines and cloaked units to create traps.