back in the day i've sold/installed the TV you are referring to.
best bet if you want car audio speakers is to build bookshelf enclosures for them. will sound much better than the baffle the speakers have now (which should be two-way with separate woofer and tweeter).
yes, there is a ton of room inside for mounting other stuff. but a home theater receiver and bookshelves/towers will blow away anything else you could cobble together inside.
that said,your project will work and will probably sound better than it does now.
FYI - the TV breaks into to pieces: top and bottom, for easier transportation. you remove the front screen, then the bolts around teh side/back, and lift off.
if you don't have the amp/power supply already, do yourself a favor and buy a receiver. even a standard stereo receiver will do wonders for simplifying your project. then you can focus on the speakers. for a budget, a Pioneer SX203 or SX205 can be had used for under $50. and i've been running car audio speakers off a SX203 for 15 years, my garage has one running Eclipse PS components and HSL 12" subs - and it rocks.