Something based on a chip like a TDA2030/2040 or LM1875, and delivering 12-15W can be quite loud enough if you keep the following considerations in mind:

1) Efficiency of the cabinet and speaker can often make a bigger difference than doubling or even tripling the wattage.  A great many lower-cost amps come with speakers that could be larger or more efficient, and/or come in cabinets that are kind of slender or shallow.  Sometimes, something as trivial as closing the back off more, or even just moving the baffle ahead a bit so that it isn't recessed, can elicit higher performance, and especially more of the bass that creates the sense of loudness.  Similarly, trading up from an 8" to a 10" or even 12" speaker will net you more apparent loudness.

2) Your power supply should be robust enough, in terms of current capacity, to support the amp.  Forty watts with a wimpy supply will not sound any better than 10 with a robust supply.

3) Manage your signal levels such that each stage delivers as much signal as it can while still preserving a bit of headroom.

You're right, it can work the other way too.  I have to head out of town, but I'll try and post a pic or two when I get back.

I picked up one of these cheap at a music store yard sale, and was trying to spruce it up (dusting, pot cleaning, cabinet re-do).  While it would be within my capacity to reverse engineer it (its a TDA2030-based unit), it's a royal PITA to disassemble and reassemble.  Right now, the barrier separating it from functionality would appear to be an above-the-board connection between some soldering terminals that I foolishly kept no notes on.

If you have a schematic, or a gut shot or can simply tell me where thew wires go to on yours, I'd deeply appreciate it.

The old 1973 Jack Darr book, recently re-published by the folks who bring you Audio Xpress, was split about half and half between solid-state and tube amps.  Most of the solid-state amps, however were Gibson, Harmony, Wards-Airline, etc, with none of the other makes you refer to.