Tony, I ran 185 70's on a square arched Sprite, with minor rear rub issues under hard cornering, but didn't have a panhard bar. I've got 175 70's on a round arch Midget with no problems at all, and what appears to be plenty of clearance for more tire, so the Bugeye should be about the same.
Both of these setups are on the Minotaur 13x5" wheels, with no spacers used to widen the track.
Watch the clearance between the tie rod end and the front wheel, as you may have to trim a bit from the exposed end of the stud to clear the wheel. If you use tape weights for balance, make sure they aren't in the path of the tie rod, as it pops them right off. (The voice of experience. /ubbthreads/images/graemlins/grin.gif)
Jeff