It is usually AC, 12v RMS.
That is why I thought converting this to DC might actually bring up the voltage a bit.
You lose .7v in the rectifier but you are then approaching the peak to peak instead of RMS. The voltage drop thing might still end up eating all of your gain (that is one of "them engineer'n" things).
A high tech solution would be a wide mouth 12v inverter power supply that works down to the 7-8 v the OP has.
