Great idea Calico!  It may be obvious, but I've been doing the opposite - 5-10 minutes w/o the shield and then putting the shield on because it hurts.  Using the shield first would probably work better.
The LC initially asked me to try w/o the shield once a day and then she asked me to up it to twice.  She says the baby's latch seems better on her finger, but I'm doubtful that anything has changed.  However, they say it could get better after ~4 weeks, so I will keep trying.

Here is what I'm currently doing, in case anyone has similar issues and is curious:
BFing all day mostly w/ shield
Pumping at dinner time (5-6 pm) because that is when milk supply is lowest and baby gets frustrated
BFing again
Pumping before bed and once overnight because baby doesn't have to wake up so much to drink a bottle.  I think getting a nice easy 3 oz bottle helps her sleep longer.  I got to sleep for two 3 hour stretches last night!

I'm starting to think about putting more effort into weaning DD off the nipple shield.  It suddenly occurred to me that she may feed a lot more quickly without it and then I wouldn't have to be up for nearly an hour in the middle of the night once I'm back to work.  (Assuming she wakes up in the middle of the night.)  I have 6 weeks to go, but I'm already starting to stress!

Any tips?

I'm supposed to try going without it twice a day, but I almost always forget.  Did it yesterday and let me tell you that the milk seems to come out a lot more quickly without the shield.  Instead of sounding like suck-suck-suck-suck-gulp, it sounds like suck-gulp-suck-gulp-suck-gulp.  Unfortunately, it still kind of looks like she isn't latching correctly, but I'll keep trying.