Yes, very strange they put a second transformer mount on the other side. Maybe they made a mistake and decided to put it on the other side. I don't think it's for a future upgrade, because if they decided to add a rechargeable battery I think they would just put it in the existing battery compartment.
Interesting that the Muse claims 80 watts, but the Aiwa says 40 watts. Maybe they mean 40 watts per channel? But that would be unrealistically high. I suspect the true RMS output is lower.
Can you please take measurements of the shell? I don't trust published dimensions, they are often incorrect.
Do you detect any vibrations or rattles from heavy bass? Anything inside rattling?