An other long term option would be to use GTC as a utility token and create a new governance token.
The virtual token used for CowSwap seems to be an idea we could learn from.
r/ethtrader donuts is another case study that could translate well to address this very fair concern.
From Donuts FAQ:
Q: What is CONTRIB?
A: Whenever a user earns donuts, they earn an equal amount of CONTRIB. CONTRIB is a separate token and is non-transferrable. It essentially shows life-time earnings, even if a user has sold their donuts. It can also be used to potentially restrict some actions to users that earned their donuts, rather than purchased them.