That sounds strange. The mirror up mechanism is really just an extra shutter release: it's a spring loaded see-saw with a hook under one end, which holds the shutter release mechanism so it won't fire even if the normal release is pressed. With the selector in the normal position, the selector itself presses down on the other end of the see-saw, keeping the hook from blocking the release. In the mirror up position, the selector is lifted, letting the spring tilt the see-saw so the hook grabs the release. You then have to use a cable release fitted into the center of the selector to tip the see-saw over and release the shutter.
From your description, it sounds as if the shutter behaves as if it were set to "T" when the mirror up mode is selected. How this should happen I have no idea.
Anyway, if you've never been inside one of these lenses before, and you value the lens highly enough to feel that a professional CLA is worth it, do so. If you're mechanically inclined, would like the challenge, and won't mind if you screw up and don't get the lens back together, possibly ending up with a more expensive repair job, or even sufficient damage that it's no longer worth it, taking the lens apart can be fun. A lens spanner and 0 and 00 size philips head screwdrivers are all the tools you need.
Lots of pictures of the insides of RB67 lenses here:
http://logojoe.com/RB-RZ/
I've got a replacement shutter fitted in that 180 now, and the original soaking in heptane to get the dried grease and oil out of it. I noticed too late that the new shutter doesn't work properly in T mode, so I'll be refitting the original one and then doing a CLA on the one I thought was good. Then, I'll have a proper spare for the next time it's needed.
-tih