I think you need to hook one side on and stretch them over, I don't think you can push them on. I remember that I had trouble with the rear dust covers. I think the problem was getting something between the wall of the caliper and under the rubber in order to stretch it.

Maybe try something like a small Allen key when there's slack.

For rubber repair, you could try one of the various GOO products in the adhesives aisle in the big box stores. But in your climate and road conditions, maybe another $20 for two more gaskets might be prudent, assuming you didn't cut more than two of the covers. Keeping water out will protect the piston. The rubber may be coated with light powder or something that may keep the adhesive from sticking.