Hey Barret, just stumbled across this thread after having done the exact same as you this weekend due to the same symptoms (though I also broke apart the check valve, so will be replacing that

). I read another thread where a user tested the check valve and the gas cap, and they believe that the check valve is indeed correctly oriented and for positive pressure, and the gas cap is what's used to equalize negative pressure (being higher up it's better if it pulls air in).
I'm at the stage where I think I'm going to buy a new gas cap and check valve (I don't have the hose diameter to check my gas cap, and it's probably original i.e. 30 years old), along with replacing all of the fuel lines as they're impossible to take off without breaking them. But having seen this thread I'll also be checking out that screen, though I agree with you on not understanding how it could cause vacuum.
I wonder if anyone knows the bolt sizing details for the seat bolts? I absolutely destroyed my tamper-proof ones trying to take them off hahaha
Please let me know if you've done anything since which fixed the issue.