From a technical perspective, stkIDLE is based on veCRV model which, as you know, makes it not-transferrable. It makes also the contract base immutable, so it wouldn’t be feasible to attach an NFT to any new or outstanding stkIDLE.
Another way to have ‘liquid’ stkIDLE for new stakers is via integration with VeTokenFinance (in progress) or StakeDAO liquid lockers. This is similar to Convex<>Curve or Aura<>Balancer relationship. This kind of staking is irreversible (your IDLE would be locked perpetually and you won’t be able to withdraw it) but the token would be tradable if there are AMMs pools for it (eg on Curve/Balancer/Uniswap/…), along with other benefits.
Current stkIDLE holders have to wait until the lock expires to claim IDLE tokens.