Adam -
Even though this is an old post I had to chime in.
I don't have a Riviera, I have, and restored, a 1967 Pontiac Tempest.
The Tempest came to me with a retro-fitted AM FM Cassette (junk) that someone had cut the dash to fit. The sound was awful and I ended up welding in a new panel.
I found a stock OEM radio here - https://www.vintagecartruckradios.com/tempest-lemans-gto-1961-1975/ and it bolted in and I've been pleased that my Tempest is as original as it had come from the factory.
I'll bet that you can find a decent stock OEM radio that will look great and will sound as it did in '63.
I always thought that part of the charm of a vintage auto was to enjoy things as they were when the car was made. If you want modern sound - get a Toyota.