I had to do that a lot with my old mower. When the grass was really high, I would also run only half the mower over the tall grass, with the other half over what I'd just mowed ... more mileage required but less strain on the mower.
I haven't had the choking problem with the new mower, probably because of its extra horsepower .. 6.5 vs 4 for the old mower. But I haven't run it thru wet tall grass, which will be a real test.