Felipe,
Go for it! I think that you will find that your supply voltage will drop under load conditions...
There is no such thing as a perfect voltage supply (0 output resistance, voltage invariable under load); all real-world power supplies include series resistance (for example, from the 10s of metres of wire used in the transformer, etc).
Remebering that Power (RMS) = (Vp X Ip)/2, we can rearrange to get Ip= 2 x Power/Vp = 2 x 55 / 36 = 3.06Amps (peak) or 2.16A (RMS)
If the power supply resistance is 0.2 ohm, and the average current through the power supply is 2.16A, then the voltage on the rails will drop 0.2 x 2.16 = 0.432V. Your experience may be more, it may be less, but either way, it will be close enough to 36 volts to not worry the LF output stage.
Please let us know what you think when you are done!