I'm running Ultegras. They are tight getting a 25 in and out with the cam open, havne't looked to see just how close the clearance is in the top. I assumed I'd need to rims because I'm pretty sure I could not get an inflated 28 on and off and still have the brakes adjusted.
Yes, unfortunately it wouldn't matter if you got new wheels because they would still need to be 700c (622mm) in order for the rims to reach the brake calipers.