I am keen on this idea, but i propose the other way around which might be easier for devs too, frontend during claim to have another checkbox ticked by default:
Convert ETH/AVAX to GMX
Link this up to a aggregator (e.g. 1inch) and swap the coin into gmx enabling seamless experience for the user.
This would allow users to choose between eth/avax/gmx, and not kind of forcing gmx onto stakers, still has the real yield narratives and holding eth/avax in the contract in theory would be less volatile than just pure gmx alone.
essentially does a twap buy in to gmx too, since everytime a user claims then their respective eth/avax is converted into gmx instead of every wednesday the contributors have to convert all the consolidated fees and purchase gmx from the market.