Ground loop issue, looking for temp solution via battery powered device ?

As it's just the amp that's producing the hum, and not your other gear (i.e. your audio interface), and given that the amp performs better elsewhere, that leaves the circuit that you amplifier's plugged into as the probable culprit. 
 
There are two possibilities. One is that the circuit is improperly wired, the other is that there is something else connected to the same circuit that's injecting noise into the line, such as a refrigerator.
 
If the problem hasn't always been there, and just recently began, you can probably eliminate the first possibility. You can confirm that by taking the amp to another part of the house and plugging it into a different circuit. Just make sure it's really a separate circuit - you could make sure by turning off the outlet you normally use via the circuit breaker.
 
If the problem has always been there, then it's likely the circuit is not wired correctly. Your electrician should be able to test that easily if he has the proper equipment. Have him verify that three wires are coming to the outlet and that the ground wire is connected. He may have a tester that can indicate whether the ground wire is too short, i.e. daisy-chained to another outlet as opposed to running all the way back to the neutral-ground bond in the service panel.
 
If all else fails, you can get an isolation transformer. In many ways, that's the ideal solution. Get one hefty enough to handle all of your audio equipment and plug everything into it. That'll solve all grounding issues and most EMI issues, and many RFI issues.

I tried #3 and #4 but instead of using battery or power adapter, I power up the Tascam with a usb power bank via a USB to (Sony) PSP type cable. This setup is great as it's truly portable without having to worry about buying batteries and the power bank will last for a very long time. I've been using it for about an hour and it only used up 1% or less charge.
 
I've exported the backing track from Sonar to Tascam and everything works perfectly - it's so nice not hearing any noise at all and I can concentrate on my guitar part.

I picked up a couple of passive direct boxes, and put them in line to my speakers, and that knocks out anything I  had been hearing,
 
I will look at picking up some flavor of isolation transformer, in a month or 2, as I have been chasing off dollar vultures for the past couple months - and they are likely going to remain for at least the next couple of months too.
 
Oh Well, at least things seem OK now, for the most part.
 
Bob Bone
 

Definitely check the USB cable as Cactus Suggests.  I had a very weird ground problem that cropped up when I installed new KRK R5 monitors last week.  Weird because it only happened using powered speakers from the balanced outputs, and the frequencies where not simple AC harmonics.  On top of that, engaging phantom power produced a really pronounced hum cycle.  I tried changing all the leads, flipped the speakers, used different isolated sockets all to no avail.  Then I changed the USB lead to the powered Audio Interface, using what seemed a better spec'd one I was using for my controller keyboard and that cleared pretty much all of the problem.
 
Worth a shot - this was certainly a cheap option for a fix!