While it could be a carb problem, don't rule out a cylinder problem. Are both cylinders firing? Without knowing any history for the engine, I'd do all the basic checks to make sure the engine is in good health and here, in no particular order are a few things you can easily check. Is the compression similar between cylinders? Check that by removing one plug at a time and while rotating the engine through compression, do they feel relatively the same? Has the engine ever been overheated which wouldn't be uncommon in a scale plane where users do their best to use as small of air inlets / exits as possible? Perhaps a stuck ring if that is the case. You might want to remove the mufflers and inspect the piston / rings. Zenoah rings seal quite well so if there is excessive staining on the piston skirts below the rings, suspect stuck rings .... and especially if one piston looks different than the other. From there, confirm that both cylinders have good spark and that they are indeed both firing. You can confirm this by simply touching the cylinders / mufflers after a short run. They should be of fairly equal temperature. Check all bolts for being tight, etc. Has the engine ever been damaged by a ground strike? Again, if you remove the mufflers, turn the crank just until the pistons start their upward movement. Are both pistons in the same position on both cylinders? If not, the crank may have slipped on one or more crankpins and need repair or replacement.

Again, just performing a basic engine inspection while confirming that all systems are OK should reveal the problem. I'm not familiar with the prop you are using so it might just be way more load than you think it is and there may not be any engine problem at all. These engines like to turn up and will pretty much fall on their faces performance wise if overpropped. A typical 24-10 you suggested will probably turn around 6800 though the engine will perform its best if propped for 7000 or more. You just have to find the best compromise prop that will pull your airplane the way you want it to perform while keeping that Zenoah happy. A 24-10 usually falls in that compromise range.

Regarding carb kits, the GT-80 uses a Walbro WJ-64 carb and the rebuild kit is a K10-WJ available from any small engine shop or a multitude of Ebay or other online sources.

Plug gap isn't critical and you should be fine where you are at .024" or so.