Battery Power & Power Amp

Your Bryston 4BSST power amp is a 300 w.p.c. powerhouse, that runs on standard 120 volts. The Red WIne Audio Black Lightning hugh current battery supply is designed for low power consumption, low voltage (5 to 20 volt) components. It will not power a 120 volt, high current amplifier. It would take some huge batteries, and plenty of them, to power such an amplifier. You would be better off buying a power regenerator type of power conditioner if you insist on "clean" power for the Bryston.

An IME battery from the hybrid automobile can supply power for 4bsst. The price is near $5k + the price of good designed fanless voltage converter. Voltage conversion that goes directly to the DC portion of the amp is smart way to utilize the battery capabilities bypassing all rectifiers which may run you to another 4-digit price tag.
Looking at near $10k battery box or more. Battery from Tesla would run over $20k itself, but certainly would last substantially longer. BTW forgot to mention battery charger which don't have to be much of an expensive portion.