This is a very interesting topic.  If a solution was found, a much better, easier, more convenient implementation of Bitcoin would be possible.

Originally, a coin can be just a chain of signatures.  With a timestamp service, the old ones could be dropped eventually before there's too much backtrace fan-out, or coins could be kept individually or in denominations.  It's the need to check for the absence of double-spends that requires global knowledge of all transactions.

The challenge is, how do you prove that no other spends exist?  It seems a node must know about all transactions to be able to verify that.  If it only knows the hash of the in/outpoints, it can't check the signatures to see if an outpoint has been spent before.  Do you have any ideas on this?

It's hard to think of how to apply zero-knowledge-proofs in this case.

We're trying to prove the absence of something, which seems to require knowing about all and checking that the something isn't included.