So far, I've proven that about 12% of the code behaves the same when executed single-threaded.
Dude, this is a database.
Concurrency is the source of all the hard stuff in databases.
Databases without concurrency are super-trivial.
I don't see any fundamental limitation that would prevent this from scaling up further.
The fact that you've dodged all the hard stuff is a pretty fundamental limitation.
Proving the code works single threaded is a stepping stone to eventually proving the code works under concurrency. It may be surprising, but very little of the Postgres code deals with concurrency. For the most part they've isolated the parts that deal with concurrency to a small number of subsystems. At least by volume of code, the vast majority of it is single threaded