I'll keep it short.Put it this way, I would give up Pick 8+Scharenberg in a heartbeat for Luke Parker. You are still getting back more than you are giving. Look at the history of Pick 4's and 7's, even with 2, you're unlikely to get a player of Beams' quality back...and Beams takes away the risk element.
Also, you're the one saying how big the gap between 9 and 4 is, but apparently pick 7 is the same as pick 3 when it suits you
Burgoyne = pick 9 and pick 16
Beams = Pick 4 and pick 20
You'd take 4 and 20 over 9 and 16 every year. Since we are probably offering a fringe player as well for the Beams trade it is pretty close to par. Don't forget he is asking to be traded you can't only accept the farm when he is trying to get home for his sick father.