What's the best way to reduce the wattage on an audio amp output?
I would recommend configuring the amplifier for a lower closed-loop gain. The amplifier board you linked to is built around a Diodes Inc. PAM8403. You can pull the datasheet for that part to learn how to configure it's gain.

Unfortunately, the datasheet is not very clearly written. It gives the closed-loop gain of the amplifier as:


  AVD = 20*log [2*(RF/RI)]


However, "RF" is not identified on any schematic. Based on the verbage, though, I think it is safe to assume that RF is the feedback resistor inside the IC, with a fixed value of 142kohm. "RI", in the above equation, is the sum of the internal input resistor, which has a value of 18kohm, and any additional external resistor in series with the input to the chip (labeled RI on the front page application schematic).

What this means for you is that you probably want to add additional resistance in series with the input to the amplifier board. If there is already an external RI on the little board that you have, then try replacing it with a larger value until you are satisfied with the volume range. If there is no footprint for it on the PCB, you will have to find a way to kludge the resistor into the path - maybe splice it into the connection between the tone board and the amplifier board.

It is worth noting that your tone board is passive and, thus, has significant output impedance itself. In this way, it is possible that the tone control will interact with the gain of the amplifier and vice-versa, altering the control law of the volume and/or tone potentiometers. I won't offer a complete explanation here, but this is something to keep in mind if experimentation yields confusing results.