Thanks for the response, dklein.
So I did what you suggested: mic > mic-in jack on the MD player. I recorded a few seconds of myself trying to strum the guitar (just learning how to play it), and upon playback, both channels are fine. Testing ear by ear/channel by channel, the left and right sound similar, and the right doesn't have the quiet/muddiness of the show I taped last night.
Then I went back to the previous setup (mic > battery box > line-in MD), and the problems were back: faint buzzing through the recording, softer right channel.
Now I've just tried the other setup you mentioned. I used the line-out on my portable discman and connected it to the line-in on the MD recorder. Watching the levels on the screen, they aren't equal - the right channel is off by some amount of dBs; like the left channel would be going above the -12 db mark, but the right channel wouldn't. I should note that I don't the right is stuck, since it did go over that mark when I recorded last night, but it still seemed to be lagging behind the left channel. And listening to this recording, I think I can still hear the differences, it's just not as obvious.
So this probably means the problem is the line-in on the MD player, right? I wonder if it's just my unit, or if it's true of the RH-10 in general...
Is there anything else I can do right now, or just wait until I can try the original set-up (mic > battery box) but to the line-in on the NJB3 (whenever that arrives)...
Thanks for the help!
ETA - Watching the levels as I tried using the mic-in, they both seem fine and even, with the right sometimes going higher than the left.