Another possible mechanism could use reward weighting. Mining rewards mature after a period of time, and in a weighting scheme, the rewards do not necessarily go directly to the block winner. Instead, the protocol looks at a window of block winners, and splits the reward over that window according to the proportion of funds committed during that bitcoin block.
For example,
Bitcoin block 1 → 3 miners participate, total committed funds are 1 BTC, block A is selected
Bitcoin block 2 → 3 miners participate, total committed funds are 1 BTC, block B is selected
Bitcoin block 3 → 1 miners participate, total committed funds are 0.001 BTC, block C is selected
Bitcoin block 4 → 3 miners participate, total committed funds are 1 BTC, block D is selected
Bitcoin block 5 → 3 miners participate, total committed funds are 1 BTC, block E is selected
Bitcoin block 6 → 3 miners participate, total committed funds are 1 BTC, block F is selected
Bitcoin block 7 → 3 miners participate, total committed funds are 1 BTC, block G is selected
Say the “reward window” is size 5. When Block A’s reward matures, its coinbase reward (let’s use 4 STX as the reward to simplify things) is split amongst the miners of A, B, C, D, E – weighted by the amount of funds committed in their bitcoin blocks. So miners of A, B, D, E get ~1 STX, and the miner of block C gets ~0 STX. When Block B’s reward matures, miners of B, D, E, F get ~1 STX, and the miner of block C gets ~0 STX. When Block C’s reward matures, miners of D, E, F, G get ~1 STX, and the miner of block C gets ~0 STX.
Obviously, this proposal would alter the incentive structure of the protocol (almost any change to the protocol does) and would require further investigation, but it would eliminate the coinbase incentive for MEV.