Cable length shouldn't be a problem unless there is some severe attentuation taking place, but the multiple volume controls are going to be an operational issue no matter what. Ideally, if there's a volume control in each room, you'll want to eliminate volume control upstream of that to a great degree.

Here's one scheme. It may sound odd, but it would let you use whatever source was active at the 1050 throughout the house. First, make sure that every source you have is connected to the 1050 with stereo analog cables, even if you are using a digital cable for that source. Second, move the cables from the pre-amp output to the tape record otuput of the 1050. This will bypass all volume control at the 1050 (which will need to be adjusted to satisfy the Studio/100's) and will let you rely just on the room volume controls. If there is still a volume level problem with that arrangement, I would do a bit of testing of the cables between the 1050 and the amp to make sure something isn't wrong there.