On certain maps (Minsk, trois point etc) if you are double OKW vs Maxim spam you have already lost. OKW do not own a reliable MG counter like the Wehr mortar or sniper/Rifle grenades.
Rushing a luch or Stuka is shooting yourself in the foot because they will already be on their first T-34 by then, if the game lasts that long you need all your fuel for a Panther/Jagdpanzer.
Pretty much this. You have a REAL hard time countering GARRISONED maxims with only OKW units. This is one, if not the biggest weakness of OKW in team games (the lack of indirect fire/flames to counter garrisoned units).
As others have said, if you wait for Luchs/Stuka you've pretty much already lost.
The only real success I have had countering maxim garrison spam is with an Early AA HT. If you haven't already, forgo building a kubelwagen, as this will delay your AA HT and will be of little use against maxims.
My build when I expect/see Maxim spam is this: Volksx3 > Mech HQ > Volks.
The trick is with how you use the AA HT. if you're new to the AA HT, it might take a while to get good at using it, but once you do it can be very effective. Because the soviet opponent went T2, you should expect early Zis. with garrisoned maxims, what I usually do is park the flak HT right next to the building I want to attack. Do this on the side of the building you have control over, obviously - the whole idea is for the building to act as a shot-blocker for any Zis' the Soviet might have. This is risky, as a con rush with AT nades can seriously cripple or even destroy your HT. Have your volks nearby just out of maxim range to deter and other threats/ensure a safe retreat of the AA HT. Take note that a maxim will also steadily damage an AA HT, especially if there is 2-3 maxims firing on it (as their usually is).
If the Maxim's aren't in a building, try and setup the AA HT so that it can shoot the maxim, but not expose itself to any potential zis' positions. One handy hint with the AA HT: NEVER order your AA HT to attack a unit that you are not CERTAIN is within it's range, as doing so will cause it to setup/re-setup which can mean a dead AA HT if you did not want it to do this. Also, remember that the AA HT does amazing AoE suppression/damage, so if there is a unit just around a corner that you can not quite hit, order the AA HT to attack ground right next to the enemy squad. Once you get the AA HT to vet1 it gets smoke and you can afford to be a little more aggressive with it.
I've tried pretty much everything to counter maxim garrison spam, and this is by far the most successful counter I've tried. It does take a while to master, and it IS quite risky, but if you pull it off it works wonders.
Best of Luck!