Switch out to a high lift or bagger blade, it should create more "suction" and lift the grass blades. If my lawn was laying down, I would mower lower or more often, maybe try 3.5" and see if that helps.

That was the same thing I experienced when trying to mow at 4". I gave it up and 3.5" is now my max. height during hot weather. Because of cooler weather, I have now dropped to 3". Early rotary mowers had 'comb' shapes made into the front of the deck, but this was abandoned soon after because it really didn't do anything. 'metal's advice is correct. Inspect your blade and make sure it's a 'Hi-Lift' with the airfoils in good condition and not worn away. Airfoils on hi-lift blades wear away early and are the main reason for scrapping blades. Also, mulching, by definition, tends to blow the grass down - you get suction when bagging or discharging. You wouldn't try to vacuum a rug with a clogged bag; the air has to move to pull the grass up to the blade.

Toro, Ariens, and Snapper made dethatching rakes that were mounted to the front of self propelled mowers but they were not overly effective. I doubt that it would work at all in 4" grass, the mower would not likely develop enough power to push it.
Most mowers will push tall grass down, especially the thick, course summer varieties. A mower with good air flow such as Ariens or Snapper Hi-Vac might show an improvement. IMHO, MTD is not the best choice in your conditions.

That's an old idea - I've seen it on mowers from the 1950's. A comb could make the grass stand up IF the ground was perfectly flat and if the front end of the mower was open so it didn't push the blades back down as it passed over.

If the grass is laying flat it sounds like you are going too long between mowings.