Classic/Antique Car Repair: 1950 willys jeepster, aftermarket radio, current cut

Question
I hope you can help, I have a customer with a 1950 willy's jeepster and we installed an aftermarket radio and 4 speakers.  The car is 6 volt negative ground.  I used a powerstream 6 volt to 12 volt inverter and it only works if the car is not running.  As soon as it starts it can not produce more than 8-10 volts which won't turn the radio on.  How do I test the charging system.  with the car off the battery reads 6.2v running it drops to 5.75v.  If I start the car and disconnect the negative side of the battery the car shuts off.  I also noticed the battery only grounded to the motor and not the body.  I have gone through 3 invereters and triple checked my wiring.  Please lead me down the right path.

Answer
What are you running for a charging system? A generator and a regulator? Remember that 6 volt generator charging systems do not produce current at idle.Instead if the current cut out relay has closed when you started the engine and then return to idle the generator will draw current rather than produce it. This is one of the may reasons that we went to alternators. Now a question and then we will get to the meat of the issue. Does the radio work if you rev the engine up? With the engine running at near 1500 RPM what is the voltage across the battery? Let me know.
Brad