Don't recall the GEM being involved but otherwise yeah it's a set that needs the head unit, and amp/speaker unit, and the wiring harness to it, and the wiring out to the speakers coming from it rather than the head unit.
The thing that puzzles me is you start out stating it needs new speakers yet this swap doesn't give you new speakers ?? I'd go ahead and get the speakers and go from there, but frankly I wouldn't bother with the mach setup.
I'd get an aftermarket head unit then figure out the wiring to take sub or line-out from the new head unit, just make the amp/sub module an active slave powering only the sub.
Doing that you'd only need to run power and signal wiring to the sub, but after this much time I'd look the sub over first, maybe the speaker in it is shot after almost 20 years. Even so I like the idea of a hidden sub, not taking up cargo bay space, so I'd be tempted to gut the amp/sub combo and use the enclosure for a new speaker and one of those class D switching amp bare modules on ebay for around $10. They're not very powerful compared to most aftermarket sub amps but my aim would be full sound rather than loud, plus I'd wonder if too much sub power would rattle the trim panel.