That's a pretty sweet exchange!I'm also a 1984 baby and finally acquired a new bass from a fellow TBer in exchange for some soldering lessons and work on one of his guitars. Before acquiring this one though I searched around a lot, half-seriously, for other options made in the 80s and found the same issue with Fenders.
If you're set on a Fender I'm sure you can find something, but the mid 80s was a fantastic time for other brands - check out Yamaha, their BB basses were killer in the 80s. Ibanez, Aria, Tokai also should have some good options.
There is a listing on Reverb for an 84 P Bass, but the pickups on this look weird, and the knobs and bridge certainly aren't stock either... I'm skeptical about this one
I am more interested in a P-style bass than sticking to Fender for the label. I've played a modern Yamaha BB and was blown away at how good it felt. As long as it can get me in the range of Cake, Elvis Costello, and The Smiths I'll be happy.