I'd use 1/4 round edge moulding (with the inside corner cut away - you've seen this stuff, I know you have) between the edge of the door and wall all around the door (so it doesn't look lopsided or weird), run your wires through that down to your sensors and that will both hide and protect the wires around the door. Above the mounding, I'd notch the sheetrock, set the wires in the channel and mud over it, refinish and paint, and presto magico...
Or is you wanted to go fishing, you only have to fish to the top of the door, not the bottom...
All in all, I can't see this being much more than a couple hour project, including the time to open the bottle or 2 of cold frosty, plus the trip to the woodstore to get the moulding. Get the right kind, you don't even have to paint it...
I ALMOST FORGOT - while you're running this, run a second wire pair along both channels. Why? You an install a cheapy "doorbell ringer" button on either side of the door, and have a "open sez-me" button next to the door. I did this at the Oakland Garage, and didn't have to search down the remote every time I wanted to open or close the door. You could even hide one outside (maybe in an outdoor outlet box) behind a locl of some sort. You won't realize just how useful and convenient not chasing the remote is...