I run a pair of GX390’s, mine use General 4040G pumps. One machine is 5 seasons old, the other is 4. Each machine has several thousand hours of run time. I’ve experienced the same problem as you. I see from your recent update that your machine is running good again after another new carb. I’m concerned that a can of bad gas might be causing your trouble over and over, and it might happen again.
An excellent local mechanic gave me this tip years ago, and it has worked like a charm for my machines:
Once every month, or any time the machines will sit unused for a while, fill your empty tank with “Av Gas” and run it like normal. Aviation gas is available from the field pump at tiny airports or even hotrod shops… the type many small towns or rural counties have. I thought it was odd but I walked right up to the little terminal with my gas can and the kid on duty told me that all the local landscape companies often get gas there, too, because it cleans out the fuel system.
Seems that the Aviation fuel has no ethanol, is leaded, and has stabilizing additives. In my experience it can sit for ages and not go bad. No, the higher octane won’t hurt anything in your GX (but don’t put it in your car!). On the rare instance that I’ve had to replace a carb, I’ve realized in hindsight it was when I also hadn’t run the AvGas through the machine in a long time.
Give it a shot. It sure has helped me keep mine machines running like they should.