I am very familiar with the GXH50- I have two of them- one on a bicycle- and one on a stand-up style scooter. They are way way more powerful than the GX31- I have two of them also.
The GXH50 has about twice the real world, usable power that the GX31 has.
The GXH50's have very impressive torque- they will move me very strongly on both the scooter and the bicycle- I weigh 212 lbs and the both of the vehicles will go over 30 mph- the bicycle closer to 40-
measured with a GPS. There is a hill in front of my house- the GX31's will barely climb it- the GXH50's just power right up it.

The downside is that the GXH50 is quite a bit heavier than the GX31- and is built to be mounted from the bottom like a briggs and stratton engine. There is a lot of weight tied up in the casting of that
bottom mounting- it could be trimmed heavily for a good bit of weight savings but the flywheel is a big heavy unit also. As mentioned in another response, the GXH50 does have good intake passages that can accomodate a larger carburetor. Unlike the GX31, the passages in the 50cc are very generous to start with in my opinion.
I am using the delorto 16mm carbs like comes on the 50cc 4-stroke pit bikes. One concern I would have on a plane is I am not confident that the oiling of the GXH50 is quite up to the task if inverted for more than a second or two- otherwise, it should be fine.

I think it is worth a try if you have the sort of plane that could stand the engine being a little overweight in favor of the realistic sounds and scale-type power.
I do believe that you could get the weight reasonable if you completely broke it down to pieces and put in the time with the mill and a die grinder and just attacked everything in site.
HB