Maxim spam in 1s is a terrible idea. The second you see a second maxim as their third unit just get a German Sniper fallowed by a a mortar or so. Want a harder counter? go a doctrine with a MHT. For a Mid game continuing counter get a Half track and load up some panzer grens and or a pio squad with a flame thrower. Send this transport out any time you find an unsupported maxim drive up behind it and murder the maxim. Another thing of note is that when you decrew maxims it is a good idea to destroy them to prevent the Soviet players engineer squad from retrieving them all the time.
If you look upon the replay the op posted i would say nearly all your counters are not effective. Let start with the mortar. Its completely rng dependant and if you say your strat should not resolve around luck. The sniper will take a full 30 seconds to bring a maxim to 1 man force a retreat. that is a long time not to mention you are using a very frail unit and one fuck up and you can say goodbye to your 360 mp investment.
The HT strat works provided he doesn't have AT or guards.
But the biggest issue with the maxim is how cheap it is to reinforce. even if you hit with riflenade or a sniper or mortar you virtually cause no mp damage what so ever. this issue can be easily resolved if we double mp cost for reinforcement making the soviet player pay dearly if they use maxim spam.