I see two problems with the powered sub approach.
1) If the sub filters low frequencies from the main speakers it will reduce the load on the amplifier, but may also degrade the midrange and treble as it is another component in the signal path. Also, does your amp have a pre-out and power-in where a subwoofer crossover filter could be fitted ?
2) A REL-type sub where the sub connects to the speaker
terminals, but does not filter the signal to the main speakers will not help the amplifier at all. It may add some extra deep bass, but I don't think it will help produce higher volumes.
So I have my doubts that a powered subwoofer would be a good solution for your problems.