Thanks for the Sausage Shop recommendation. For anybody else who may be looking, we ended up at American Meat Company Incorporated, down on 4th Ave. near 24th street.
Excellent service (got me a six-pounder overnight) and the prices were amazing. The pulled pork sandwiches we made were a huge hit. I'll definitely shop there again.
Sorry this might be too late but here is my rec. There is a place on the west side of town called the Sausage Shop (not the Sausage Deli). They usually have a bunch of different cuts. Can't guarantee that they will have what you are looking for but it is worth a shot. They can usually special order as well but it seems like you are on a time crunch. Here are the details for the Sausage Shop:
1015 W Prince Rd # 141
Tucson, AZ 85705