From the pictures I'm guessing that is a chonda copy of the GXV390. I haven't worked on one. Remember, with chondas the bits that play up are the external bits that aren't accurate copies of the Honda parts: the governor plate, muffler, air cleaner, starter, top cover/fuel tank, etc. Hence I think you are likely to be correct in focusing on the air cleaner, or even more likely, the air cleaner fouling on the governor plate or linkage.
If it will run perfectly without the air cleaner, but plays up when you put it on, the air cleaner is causing the problem. I'm not clear on whether it runs properly with the air cleaner shell in place, but no filter element installed. If it still plays up under those conditions, and in view of your description of the problem, it sounds like mechanical interference between the air cleaner housing and the governor mechanism. Some part of the housing may be rubbing fairly hard against the linkage.
Please post pictures of the governor arm and governor link, Paul.
