So, while removing the rear speakers I noticed things might be a bit simpler if I removed the complete rear deck. Removing it was simple - there are three sheet metal screws that hold the piece in place. Undo these, pull the thing out, and it's all done.
The vinyl cover on the tray itself was in OK shape, but it had been cut to make way for the speakers. In all honesty, I think I won't be installing speakers any time soon, which means the holes in the original vinyl just won't work well for me. Which means I have to replace the vinyl fabric.
Sigh...
Vinyl fabric is not uncommon, but for a newbie, it seems hard to find - especially for specialied applications such as automotive stuff. At first sight, I though this would take me a few days (maybe a couple of week) just to find the proper materials to do this.
This is where google comes to the rescue: after a few hours, I had found PerfectFit Wholesalers in in Tukwila, WA (down the street from work.) These folks advertised a variety of vinyl fabrics and the such, and so, I paid them a visit in person.
Sure enough, they stocked some automotive-grade vinyl fabric closely similar to the old vinyl in the car. I ended up with some from this product line They also supplied a sheet of headliner foam which, although not an identical match for the deck padding, serves the purpose very well (and it will be hidden from view anyways.) They even sold paperboard, which I can use to replace the original paperboard tray, which is already in pretty sorry state. Total cost for materials was about $40.
I highly recommend this place for any sort of fabric/upholstery need for your automotive project.

I had to glue two sheets of fiberboard together, as they were too thin by themselves. This took about half a bottle of wood glue, and a couple of days for the glue to dry. I then used the original tray as a template, drew an outline, and trimmed the board down to shape with a circular knife and lots of patience.
Next I cut the headliner foam to shape, and glued it to the fiberboard tray with spray-on glue.







Next up - third brake light gets installed.