Hi Tim,
Yes, you would need to connect both regulators to Star Earth, no way out of that one.
No, 10-15V is too much. You need only sufficient extra voltage to accommodate the maximum sag of the amp at full tilt.
Let us assume that a 55W AKSA will do say 30V peak into 6R. This would mean that the supply would draw a maximum current theoretically of 5A, about right for a single pair of output devices. Thus, the shunt reg should be designed for 5A continuous.
The shunt element will pull the conjugate current; that which is NOT drawn by the amp, with the total being 5A. This means that we need only a small margin over the 36V nominal rail voltage, but in fact at full power the standard supply would drop to about 33V under load. So, giving the shunt element a full 7V of margin, we must use a raw supply of 40V, call it 42V as this is a 30-0-30Vac trafo.
Now, with 42V, we can sink to 36V under load with a six volt drop, which will be across the shunt resistor. The shunt element will pass up to 5A at this 36V at all times, falling with increasing amp output. So, this means it must be set up to dissipate 180W PER CHANNEL in the shunt elements alone.
Now, this is an improvement on dropping 10-15V, BUT, do you see the problem? You will be dissipating 360 watts through the shunt elements, spread over four devices - though more properly eight devices, giving you 45 watts at each device. In addition, you will be using a resistive shunt element to drop this seven volts; this will dissipate a constant 5A x 7V = 35watts, and you will need four of them, too.
I would very strongly recommend that you use mosfets for this task. They are VERY robust thermally.
Cheers,
Hugh