Probably not your problem, since you say the holes are on the tire side, but I was recently having strange persistent flats on my road bike and seem to have solved them with new rim tape. There wasn't an obvious tear or hole in the old tape, but it was weak over one spoke hole, so I think the tube was getting pushed into the hole at high pressure.

Anyway, something to consider if the new tires don't do the trick. Only costs a few bucks.