Since you have a power antenna, my first thought would be that the antenna motor is not shutting off when the antenna retracts. Have you tried unplugging the power lead to the antenna and seeing if the problem goes away? I doubt if its your radio itself, as if it was pulling ten amps when the car was shut off, you'd definitely be hearing some noise! Another possibility is that the premium sound amp is not shutting off when it should, although it shouldn't pull that much current with no signal.
You also mention the same fuse serves the shifter lock out solenoid. Is the solenoid staying energized all the time, instead of just when you step on the brake while the car is in Park? Can you shift out of Park when the key is off and your foot is off the brake?
Just some ideas, hope something works for ya.
