Dedicated Line Advise

Definitely run both lines on the same phase/leg otherwise you will most surely get hum form your system.  If you don't have enough room on one side, you can just move breaker's around.    One of the best "upgrades" i did for my system was completely reconfiguring the electrical panel, tightening up all the connections etc.  You can see a more detailed description on my systems page here on AG.

Good Listening

Peter

Minorl,

Having worked on this issue extensively with many different systems, the chance of getting ground loop hum when powering equipment from the two opposing phases in your panel is greatly increased.  While I agree that in theory it should not matter, in practice in most cases it does.  

You mention that your two amps are powered from the same leg in your panel while your front end is powered from the other leg, however you also mention that

"My low level equipment are all connected to a Transparent Audio Power Isolator 8 line conditioner, then via a dedicated line back to the panel."

This could be the one reason that you don't experience this phenomena, as an experiment why not try to eliminate this one and see (hear) what the result is. 

Coming from the EE camp also

 Good Listening

Peter

Minorl,
While I agree that it is quite easy to change a breaker to the other phase in a panel - but if one is not familiar at all with electrical work - I will strongly caution about the DIY approach on this one.  For one there is lethal voltages inside the panel and even though the main beaker is turned off, depending on the design of the panel there could still be live voltage inside the panel - in my main panel the feed coming from the meter to the main breaker are still live with the breaker in its off position.

Another one I will never forget, while an electrician apprentice back in Denmark, where I'm originally from, we were called to a vacation home to install an electrical outlet for a TV.  Initially the owner had tried to install it himself, even though back there its actually again the law.  Also every house is fed with three phases and neutral, 220V from neutral to each phase and 380V between the phases.   He managed to get 380V on the outlet, and there was an empty TV stand in front of the outlet :-)

Good Listening

Peter