In the GX series, is the number the displacement? (gx200, 200cc, etc?). If so you probably wouldnt be able to even fit a 240 piston in a 200, doubt there is enough meat in the sleeve to bore it enough, even if there was your liner would be too thin.
Taken off another forum.... " The stock sleeve just isn't that thick. You hit aluminum at about 2.750" bore. That's way to small to fit that piston"
Then it goes on to say that SOME CLONES MAY ACCEPT a 240 piston but the liner will be THIN at the bottom..
"I had a look at my shelf in the workshop.
The block that I bored for a GX240 piston was a clone block indeed.
I did not know the Honda sleeve was thinner at that time. Just did not want to waist an expensive Honda block."
I think you would be better off building some girdles and finding a turbo than playing the "how thin can that bore be run?" game. Though there is no replacement for displacement, there is a most excellent substitute called boost.