I use Dundee from time to time, just as you are describing.
I agree - IAPs from the West so most likely a circling approach. As yet I've never actually used that.
Is it that hard to just go around Edinburgh? That's what I always have done.
Prestwick is the other side of the country but affordable, friendly, and has excellent public transport links as well as the best runway availability in Scotland and more IAPs than you can shake a stick at. That might be the best alternate. After all you don't need to actually use your declared alternate if there's a better choice at the time.
G