Black Point Compensation is only relevant if you're using a colorimetric rendering intent (like Relative Colorimetric, which there's no good reason you shouldn't use if you want to, unless Mirage lacks BPC for it...). With Perceptual you shouldn't have blocked up blacks, since it is, as the name implies, a perceptual matching algorithm, BPC is essentially built in. In Mirage the setting is probably wherever you choose "perceptual" -- you likely have an option for "Relative Colorimetric" and one for "Relative Colorimetric with BPC" maybe instead of a checkbox like photoshop uses. I'm sure it's in there, but if your problem is happening while using Perceptual then it points more towards the profiles themselves, or some other mix up in settings. Either way, since you can make your own profiles... make your own profiles, they'll be better.
As far as remote desktop software is concerned, I would never expect to get accurate color-- you're essentially sending video thru a live h264 encoder (or whatever other codec is being used by the particular software you're using) so you're susceptible to all sorts of weirdness that can occur with video encoding/decoding, and likely the dreaded quicktime gamma bug as well, if you're using ARD.