I second cutting holes in the sheet rock, the fiberglass is going to get wound up on the drill and cause a real problem. The flex bits that are like 10 feet long can be really hard to use because they tend to whip a lot, would certainly be my last choice of tool to use.
That said, can you drill a hole big enough to put a piece of plastic or metal conduit through, then feed the long drill bit through that conduit to get the farthest hole created? That might prevent the fiberglass from wrapping around the drill.
I have a bunch of work like this that I need to do, but time and other issues have stopped me so far. But this summer I need to run cables for cameras and wall work is going to be one of the tasks to get all the runs down to the NVR. Need to bury some cable too, which is rarely fun.