Romy and friends,
Reading about the sensitivity of your system to electrical power supply problems reminds me of the days when I used to make my own equipment as much for the learning experience as for the final result.
One of the mundane things I learned is that standard audio equipment, including shielded cable connections, did not (and possibly still does not) follow good GROUNDING practice. You connect the stuff in the usual way and you are bound for problems.
The sensitivity of your low-level equipment, the success of using battery supplies on some sources and the inability of line filters and conditioners to alleviate the problems without causing other problems suggests that you might look again at the grounding in your system.
Remember, a grounding problem does not always result in hum or any noise in the absence of signal. Grounding problems are dynamic and disturb the signal and so can masquerade as or exacerbate a power supply problem.
At the risk of stating the obvious and trivial to experienced practitioners:
1) Cable shields should be grounded at only ONE END, otherwise you are providing multiple ground connections between pieces of equipment.
2) The single cable shield connection should be connected to the internal central ground point by wire not by chassis. Usually, the cable shields must be disconnected at one device's connector.
3) Sometimes, one cable shield of a stereo pair is connected at both ends to make the ground connection between devices but this is not as desirable as a single separate wire for grounding each device to an external central ground (STAR grounding instead of cascaded grounding). Remember a cable shield is intended to reduce noise, not carry signal or ground.
4) The system as a whole should be carefully grounded. Sometimes household grounds are inferior and a high-quality separate connection to a good outside ground is needed (a subject in itself).
5) You may have a stray voltage problem.
6) Your audio system might benefit from a dedicated power line, isolated from other household appliances.
7) If you live in an apartment building consider moving.
Grounding, so basic and simple, can be a subtle and tricky thing. It is important but cannot be perfect and therefore always suspect. The more problems that involve the low-level equipment the more I would suspect faulty grounding and shielding at least as a contributing factor. It should be obvious that the more extensive the system the more likely the problems.
On the other hand, where grounding turns out not to be much of a problem, I wonder if the new high voltage battery technology used in hybrid cars might be useful at least for the true audio obsessive.