Yeah, what he said. if you can't find them locally, Rivendell (www.rivbike.com) stocks three or four types. i have about 12,000 miles on some MKS old-style pedals from there, and i like them a lot.
I can't tell from the description exactly what the problem is with your current pedals, but could you secure the straps with a sheet metal screw or something? Just drill a little hole and run a tiny self-tapping screw into it, through the strap? Or do something with a zip tie?
If you buy new pedals, thread the strap through one side and give it a twist before you run it out the other side. That will keep it from slipping.

EDIT: Sorry for repeating information from another post--didn't notice it when i skimmed the thread. Those MKS pedals are the same ones I have on two bikes. Cost about $40 from Rivendell, probably less elsewhere (I like Riv and try to support it, even if it costs a little more). No problems ever.