Having spent a while stuffing 28/32mm tires into older sport bikes ('just put in the biggest tires that'll fit!'), I've found the tight spot to be the rear brake bridge of caliper, not the stays.
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You know it's going to be a good day when the stem and seatpost come right out.
(looking for a picture and not seeing it? Thank the Photobucket fiasco.PM me and I'll link it up.)