Harry, we have the same problem here with rain every 3 days keeping the ground soggy. Whatever done with my push mower is taken off the factory mulching blade and installed a regular straight bar blade, set the mower in a higher than normal position and cut my grass. Then a couple days later ( between rains) after the cuttings ha be settled in a bit, I lower the deck a bit more and mow again. Grass doesnt clog or clump as bad that way...
but ymmv though