Wes,
I installed a lot of CB's and car stereos back in the 70s and 80s. Don't know what kind of head unit you have, but I'll assume it's a single DIN model. It sounds like it could be a short in the wiring between the head unit and speakers. Loose wires under the dash or loose connections on the speakers could cause that. You've got a lot of other priorities it appears, but when you're ready to tackle it, here's what I would recommend:
Get a pair of replacement speakers that you want to install
Pull the head unit and connect it to a spare battery to bench test it
Strip the wires from both speakers and the head unit
Just twist them together and make sure it's tight
Fire up that head unit and put in a CD (or cassette). Do not use the radio as the reception will be poor with likely static
If it all sounds good, mount the speakers in the doors and use terminal connectors that fit nice and tight. Use 12 gauge with mostly copper strands (cheaper wires have more aluminum), do not splice the wire between the speakers and head unit.
I highly recommend soldering the wires from the head unit to the speaker wires.
Use plenty of zip ties to keep them together along the run and find some other wires or supports under the dash to keep them from dangling. There should very little, if any, sway along the wire run.
Crank up them tunes, man!
As a side question, I would be interested in learning what you selected for your muffler and why. The exhaust system on my Rampage is a down the road project.