None of the above. . . . !
So you've got a small budget and an 80's cover band. Who cares what gear they played in the 80's. . . . actually for most bass players it was what they played in the 70's, and what they all went on to play in the 90's. You've already got the best bass, you don't need to make it 80's, whatever that means. You don't need to spend anything. Your budget should be safe.
What worked for them, me and my guess, you, is "One bass to play them all."
ps
If you really have to blow your budget put a set of Bartolini pickups in your Precision. That is what a lot of bass players did in the 80's. . . me included.