As @Riplin was saying..

You can coordinate the cut through transactions off-chain using a trustless centralised entity - Layer 2 style.

And a decentralised protocol could work @TierNolan but it's also really easy and secure centralised.

So lets say

A -> B -> C -> D

A pays B who pays C who pays D

Cleary the best outcome is A pays D.

A -> D

A,B,C and D could all be members of this 'CutThrough' website.

They perform their 'desired' transaction to another member of the website - but nothing gets posted onto L1.

The Website crunches the numbers and calculates what the most efficient payments are given the set of transactions it has received over a set amount of time ( hours/days ) and then coordinates with those Users to create the appropriate transactions.

The Users would all have to agree, signing something and sharing so that all parties concerned were happy that everyone agreed and then the 'final' transactions are posted.

The incentive and advantage is fees and semi-better privacy. Reduction of fees as less transactions are broadcast. Privacy as no onchain transaction to show it happened - although the entity knows of course.

These fees would be spread over all the users in the cutthrough - so that ad extremis all the users payed less than they would have done. As well as all the benefits already mentioned above to the chain, and speed etc etc.. Win win. And you don't have prior bigger juicier transactions to tempt the miners with as there aren't any.

One solution could be to have a small Eltoo/Lightning channel open to the central entity. Then it could coordinate splitting the fees, and take small amounts from all the concerned parties off chain, and then pay them itself for every L1 transaction.

( This would be different to having a large Eltoo channel since you could be payed and pay a lot with only a tiny initial sum that only needed to cover fees )

At no stage can anyone take anyones money and the worst that can happen is you are delayed before diving back to L1 yourself and completing the transaction as you would anyway have done.

If you could get a 50% reduction in overall transactions.. that's like a blocksize increase x2.. not bad.