Have you thought of doing an amp with the LM4780?
Yes it is a good chip but not as easy to get as the LM3886 and also more difficult to heatsink well enough to keep the thermal protection from cutting in earlier than 2 x LM3886 just due to the surface area in contact with the heatsink. But would be great for a compact active monitor.
So, quality wise, this would not be out of place pushing a pricey set of speakers for some high quality sound, yes? I see plenty of chip amps getting around these days, all with good figures/specs.
The LM3886 amp is good and would take a lot more $ to get a small percentage better. Still the largest percent of error is in speakers themselves.
What the heat issue like? Do I need to bolt it to the Eiffel tower or anything?
No the amp runs in AB mode so it can get away with medium size heatsink but always use as much as you fit easily into the given area. A 300mm length to radial fin heatsink will look after 2 amps running fairly hard all day.
What the transformer current rating? How about the bridge rectifier?
A 160VA will do 2 amplifiers running as a stereo pair or if you are the overkill type then use 300VA. We use 35A 400v bridge rectifiers just because they are only about $5 and if you short anything the fuse will blow before the rectifiers.