Took me a long time to get barre chords, and can't do them well too long on a guitar with tough action. But that Bm that Mudlark mentioned brings up another option--muting in barre positions. Depending on what you're doing you can use them different ways, but the idea is instead of holding the barre you simply mute, and hold down a triad or more. Be careful of harmonics in those 5, 7 positions. It can have a nice sound for some things.

People tell me I'm "almost" an idiot savant, all the time. If I've understood you about your capoed c-shape--do you mean the high-e-which-is-now-a-G string? That's the 4th, or more exactly, 11th you're holding down, adding to an Eb. Eb11? Or, do you mean the g-string which you are still calling the g-string though it's Bb? Then you are adding the maj 7th and the sixth. Others are more precise than I about names reflecting the sequence/order of the notes--Mark seems right on it--I think it might depend on how I sound it, and am a bit of a shirker--I think of it either as just as my cmin sus 2 but with the Eb bass instead of the C, or as the Eb maj7 with the 6th, depending on what I was using it for, or if I was even thinking about it.