I forgot to mention the reason why it seems these blocks must constitute part of the main chain and cannot form some sort of asynchronous/synchronous 'chain on the side'.

It seems to me that it cannot be the case that 'chain #2' falls out of sync with chain #1, otherwise one or both of the chains become useless as a temporal ordering.

So the miners on each chain seemingly must be aware of the transactions on the other chain, which effectively means that you do have a single chain in which the 'canonical status' flips from #1, to #2, and back to #1 - but in order to trustlessly know which chain is newer, the prev block hash must be included, which means that you effectively have one chain.

If there's something I am missing please feel free to trash me.