Here's what I would suggest:
1. Two programs, Skype and Audition. Nothin' else. (Unless MP3 Skype Recorder counts as a third thing, in which case, that too.)
2. Record your audio locally in Audition, and set up MP3SR to only record the co-host's audio, not both of yours.
3. Upon completion, save off a copy of your local recording, just for safety. Then find a "silent" part in your recording — there will be a lot, every time the co-host is talking, you're not — and sample it, run noise removal, do that whole thing. The steps in order are: select a couple seconds of silence, Shift-P, then Ctrl/Cmd-Shift-P. Shift-P samples the audio, C-Shift-P opens the noise removal interface. Here's the settings I use, load that. Select Entire File. Apply.
4. New multitrack session matching your recording settings, bring in your audio. On the track your audio is on, add a quick track preset. (Window -> Effects Rack, if it's not already open.) Set it to Track Effects instead of Clip Effects, and just drop on one of the vocal presets. Try Radio Announcer Voice. It runs a quick compression on your audio, excites the highs and lows, and then runs a limiter on that for further volume management. Done. Don't even have to set it up or tweak.
5. Import your co-host's MP3. Double click on it to go into that track, run noise removal on that. Go back to your multitrack, add the MP3, sync 'em up.
6. Do your editing, if you wanna edit. Hitting R once opens the track razor tool, to make cuts in a track. Hitting R twice loads the session razor, which will make a cut down all the tracks ya got. You'd wanna use that one, because the tracks are synced now. In fact, if you session-razor cut at the point you want to start removing, and then session-razor cut at the point where you want to pick back up on things... switch back to the cursor tool and select both tracks in that "to be cut" area. Shift-Backspace. The selected area ripple deletes, dragging your remaining tracks up to fill the gap.
7. The bottom track in your stack (Track 7, appropriately enough), is the Master Track. Anything you do to that track applies to everything. There's a little Sum-To-Mono button on every track, but if you hit it on the Master, you only have to hit it once. Looks like this: ((O)) Hit that, and export.
The result is the same thing you were previously doing, only it sounds a lot better, a lot faster, with a lot less manual labor and software switchery.
Throw in a little bit of effects processing beyond this for warming you up, and it's possible you don't even a new mic.
*shrug*