Believe it or not, after I posted this message, I went back for another try at isolating the problem. What I discovered last night makes sense to me a bit, but doesn't explain why only the left channel was affected. I was getting ready to take the measurements that you suggested but decided to check to make sure that none of my other components could be the culprit. With that in mind, I turned everything off and disconnected the CD player leaving the Eros and Old cassette player in the system. After turning the components back on the hum was still there. I then disconnected the cassette player. Still there was a hum. All that was left connected was the Eros. I then disconnected that and the hum disappeared.... After that I reconnected the CD player and cassette deck. No Hum.... Finally I reconnected the EROS. The hum magically came back. Now with that information, I realized that there was more likely and issue with the Eros and not the Beepre. On a hunch, I decided to swap to a different set of interconnects. Low and behold, that made the difference. I think I may have had a ground loop with one or both of the interconnects. Since they are home made I am sure it was my own quality control. I will rip them apart tonight and see if there are any issues.
What this doesn't really explain to me though is why the issue would come an go like it did. I suppose there could be some environmental issues. I live in southern California and it was in the 90's yesterday. We don't run the air on at the house during the day so it was pretty toasty in the living room where my system is.
The upshot of this is I do believe I had a few minor issues with the Beepre's tube socket on the left side that had gone unnoticed. That has now been repaired.
If I have any further issues or if the hum comes back for some reason, I will again request your thoughts.
Project RPM 1.3, Speed box, Acrylic Platter, Sound Smith upgraded Sumiko EVOIII Eros, Beepre, Emotive XPA-2, Cambridge Azur 640C, Magneplanar 3.7i's, Dayton Audio Sub.