How did you decide that after a few passes through the field, the air cleaner was so dirty it needed attention? The only accurate way to determine when an air filter element needs to be cleaned or replaced is with a restriction gauge.
The air filter element should be close to the engine, not at the opposite end of the long intake tube. This may be hard to do on an engine that wasn't designed for a commercial-grade air filter system.
Down here all of the push mowers used to be fitted with snorkels and that includes the GXV 120 Hondas.
Now Briggs have taken over Victa most have reverted to the shite system you have been lumbered with where the air filters need to be replaced every 4th mow.
Honda marketed a snorkel for the 120, 140 & 160.
All used the same air filter and Honda recommended fitting a smaller jet although I have never done that because they seem to run fine with std jetting.
On the commercial mowers, Victa used a larger diameter tube
So you might need to use a larger diameter tube.
Note the larger tube used the same filter.
If you are needing to run with the engine choked that would imply that the engine is getting too much air.
have you checked for a partially blocked jet or emulsion tube ?
