DuckMauler,
A couple of comments here. First, on the Spoiler, make sure that you're running a good battery. Make sure your strings are not dead. Make sure you're running good amps/cabinets. Also, as Mica said, play around with the tone/filter controls to get a feel for the different sounds this bass will produce. The Spoiler is a great instrument. I bought mine used in 1984 or 1985 (I forget now) it's been my go to bass for almost 20 years. Even now that I own a Series I bass, I still grab the Spoiler for most gigs.
All that being said, you also must know that the Spoiler is NOT a Jazz bass. The tones they produce are totally different. Because of the bolt-on neck and single-coil pickups, the short sustain on the Jazz bass often gets interpreted/described as punchy. It's definitely a specific sound. I occasionally get calls for a gig that simply require that traditional Jazz bass sound. For those gigs, I keep an actual Fender Jazz bass tucked away in my closet.
I hope this helps. Whatever you do, don't yank the pickups on the Spoiler, you'll end up creating more problems than you solve. Worst case scenario: sell the Spoiler and buy another Jazz bass.