Ok, so I think I've found the answer in one of alpaca's posts:
"By the by, the whole system of having all trade routes exist as game objects needs to go. They should have an in potentia existence when a wagon is assigned but right now, the game creates n*m new trade routes for each good where n is the number of export and m the number of import orders, and puts them on the interface - insane! The worst is you can't use the domestic advisor anymore..."
I'm going to see if this works next time I play, but I'm pretty sure it's the ticket.
Update: Yep, this is the problem. The more possible trade routes there are, the longer it takes for your domestic advisor to pop up. I just had my game go from literaly like two minutes for the screen to load back down the the blink-of-an-eye after I deleted all of my import/export orders.
The way I had it set up was for every city to automatically export any and all goods they have unless they're going to be needing them, but apparently this isn't a workable strategy with the current implementation of automatic trading.
Keep an eye on
http://forums.civfanatics.com/showthread.php?p=7358651#post7358651 and there might be a more general solution along shortly, but until then just keep your trade routes to a minimum and you'll be all right.