Your vespa should be easy to get a proper date on it I would have thought. Just thinking that the px came along early 80s and the older model before that. By 84 it would either be a px or it won't.
I'm restoring an 1983 px myself with a dubious history, should be nice when done though.
Ah if only some dishonest Italian many years ago hadn't buggered about with the serial number!
I only worked out it was older than the V5 said by the size of the steering lock it needed.