Everything I've looked up so far discusses doing blood tests rather than the
urine tests. Don't get me wrong, doing urines is far easier (although not as
accurate), but maybe our vet recommeded it because the diabetes isn't that
severe, or because she knew how difficult getting bloods from this particular
dog would be.
Any help appreciated!

Blood testing catches the glucose level much quicker than urine does. By the
time the glucose level in the urine rises, the actual blood level is going to
be pretty high.
Blood testing will also catch a low glucose reading and urinary test doesn't.

My info is based on human diabeties not canine. I'm a 3rd generation diabetic.
Diabetes management is much easier when the glucose testing is accurate.

I looked at www.vetinfo.com and it had a lot of info about diabetes in dogs. It
says you can use human blood glucose monitors and the best places to get the
blood is from the lip, paw pad or ear margin. It also says monitoring is very
important in the beginning. Try the vetinfo site and see if it helps you any.

-sunny