OP, what you really want is a rim that works with the tires you are riding. Rims and tires both vary, from manufacturer to manufacturer and to a lesser degree, model run to model run. What you have now is an undersized tire and oversized rim. I'm sure they are both within spec, but when pushing the limits, the end result (what you are riding now) doesn't work. (There are also loose tire/small rim combos where it is very difficult to keep the tire from blowing off.)
My suggestion: go to a local shop with a good mechanic. Ask him/her (her might be better; the mechanic with smaller hands may well be more dialed in to this issue) and ask what wheels/rims of what is available now are on the small size. Consider buying those rims/wheels to be full time winter wheels, Your tight tires live on those wheels. Being mounted full time, they will stretch out a little more. Also winter wheels save your other wheels for winter abuse and make going for those rare nice day winter rides really fun on your summer wheels and rubber.
Look at this as placating Murphy, Murphy of his famous "Murphy's Law" If you have spent the money to have wheels that make the rare winter flat no big deal, he cannot have fun at your expense. Also hard to deal with tires/flats have no place on bikes below freezing. Yes, I now hail from mild weathered Portland but I spent every winter until I was 26 in Massachusetts or Michigan and the bike was my only wheels. I rode cyclocross tubulars, in real part because the flats were so much easier to change in winter conditions. I rode in conditions (and lighting) where needing jacks and straps just to fix my tire just to get home - well lets just say "no thanks!".
Ben