Sorry for inflicting to you all this horror, but I need to get it off my mind, so I going to use you as a therapist.
My though was: short branches of quick blocks, that needs to get reattached to the main blockchain.
This branches of limited length, have very small size and fast confirmation time.
The blocks are mined by proof of space/memory, where miners needs to use the blockchain as data for the proof.
These blocks don't have the coinbase reward, only the transactions fees, part of those needs to go to the miner on the main blockchain that will include the hash of the last block of this sidebranch to the main blockchain.
If newly mined block on the main blockchain contains some transaction used in the side blocks, the main blockchain is the source of truth, and the conflicting small blocks are discarded.
If miners on the main blockchain wants the transaction on a unconfirmed branch, they could simply take them and use them for mining the new block, thus we reach the above case.
Ideally these small blocks would serve the purpose of processing very low fee transactions.
The resulting chain is kind of a DAG.
I'm not sure of how this changes would interact with the Sybil attack
.If the proof of space, is implemented and nodes use it to verify each other during the connection, this would impose costs on a Sybil node, but in this case to prevent Sybil all the nodes should verify each other at the same time.
If you arrived here you have wasted you time
Bye