I purchased a new stead a while back. The wheels came equipped with 700C Alexrims DP17 (622x17) rims. After a few hundred miles I started getting punctures in the cheap tyres and replaced both with 700*32 Marathon plus tyres. I chose there because I wanted the ultimate puncture protection.

When fitting the M+ tyres I had problems, the tyre as I was levering the tyre on one side, it would pop off the other. Also one of the tyres blew off overnight after I had fitted it, I think the other blew off a few days latter.

That was 6000 miles ago, and the rear is in need of replacement, and it is getting urgent.

I bought a 700*28 Marathon plus tyre two months ago, and tried fitting to the rear wheel, and it will just not stay on the rim. If I get it onto the rim, then it pops off as I inflate it. So I went back to the old tyre. Last week I tried fitting the new tyre to the front wheel, and had the same problems. After about 90 minutes of messing around, it stayed on whilst inflated. I then took the bike out for a test ride, and within a mile or so, it came off the rim on both sides.

I really want to use M+ tyres, but this is unsafe. Are there any recommendations about what I can do?
I am thinking of replacing the rims, but am hesitant in case I encounter the same problems, are there any disc rims with very tight fitting suitable?

Both 700x28 and 700x32 are within the specs given by Sheldon Brown, and I am happy to rebuild wheels myself.