As you figured out, the root problem is we shouldn't be counting or spending transactions until they have at least 1 confirmation. 0/unconfirmed transactions are very much second class citizens. At most, they are advice that something has been received, but counting them as balance or spending them is premature.

The proof-of-work chain is the solution to the synchronisation problem, and to knowing what the globally shared view is without having to trust anyone.

Since 2007. At some point I became convinced there was a way to do this without any trust required at all and couldn't resist to keep thinking about it. Much more of the work was designing than coding. Fortunately, so far all the issues raised have been things I previously considered and planned for.