Every batch of tires is different, some smaller than others. On a big rim with a smaller made tire, you get the problem you're facing. I've had the opposite, a slightly over sized tire on a somewhat smaller rim. The tire just blew off with any sort of pressure in the tube.

Technique is a big help on tight fits.

If it's absolutely a no-go, I recommend Vittoria Rando tires, if you're not overly heavy. I'm 225 and ride at the max PSI for 32's.
They're a great compromise between Marathon Plus, which are a ridiculous tire, and something more performance oriented, like gatorskins. The Pro version are lighter, but have a lower max PSI still, which is an issue if you're over 200lbs or like over-inflated tires.