Most if not all of the loops include the FLIGHT Director loop and the GOSS (air-to-ground) loop because those were the loops that the controller had "punched up" (meaning, listening in through their headset) at their console, and in the MOCR, you put yourself in a lot of deep trouble by not listening if either of those two loops demanded your attention. You might notice on some loops during the accident, particularly EECOM's, that certain voices go up and down in volume. This is because the controller is changing which loop is louder and which is quieter in real time, so they can amplify information that's immediately pertinent to them and filter out chatter that they don't need to hear at the moment.
Controllers each have their own loop through which they can be contacted as well. During the most climactic moments of the accident, Jim Fucci (PROCEDURES) accidentally punches off his own loop, resulting in EECOM, FIDO and GUIDO later trying to contact him but not getting through until Steve Bales rings up INCO to nudge him.
The reason you can't hear the backroom loops by themselves is because they aren't considered a MOCR loop but an SSR loop, and the SSR loops aren't included in the MOCR tape recordings unfortunately. I think SPAN also listens in on the SSR loops but they tend to have FLIGHT punched up as well, so that makes it a bit more tricky.
And yeah, unfortunately if you want to listen to multiple loops at a time, it's probably best to download them off of Archive.org and edit them with Audacity or GoldWave to remove the silence and/or splice them together as I have done.