Best method for using a PA to drive a vibration table?
Open Loop is easy. (I worked in vibration testing for over 15 years.)
You are right, synthesize your PSD as a time waveform, normalize it, put it through a low pass filter (cut-off freq set to about 2-3 kHz - decided by your vibration table), feed it to the PA, adjust PA level control to get your average "g" level.

Most PA won't pass DC and will have a low cut-off of about 20 Hz, which could be a bummer, high frequency limit required depending on vibration table upper resonant frequency, if its electrodynamic, maybe 2-3 kHz. You don't want to unnecessarily excite the vibration table at its resonance.

Cheers