Recommended Running Shoes (for high arch)

I suggest also that you go get fitted at a specialty shoe store (for running). I have to do the same thing...coming up. I have Haglund's Deformity on both heels (boney protrussions on the back of my heels which aggrevate the Achilles Tendon), which makes basically my arch/Achilles/ankle/shins/and sometimes knees hurt. I just emailed a store in the Cincinnati area to ask if they could help fit me with shoes that don't rub the back of my foot while walking/running. That would be your best bet.
Othere than that, my college roommate got a pair of Under Armor running shoes where they actually looked at the way she was standing and how her weight was distributed on her feet (probably similar to that Dr. Scholls machine thing), and then was suggested a certain pair of shoes....they were expensive but she said they were the most comfortable shoes she'd ever had.
Good luck finding something. =D Speaking of Dr. Scholls...I guess you could get a nicely fitted pair of gym shoes and go to the nearest supermarket that has one of those machines and it will suggest inserts for your shoes specific to how your weight is distributed on your feet...worth a shot. They have a locator option on their website so you can find a store that has one.