The problem is that most of these cieling clips are only good for cielings that are between 3/8" to 5/8" thick. Now what you have is called plaster and lathe. The lathe are the wood strips and the plaster is adhererd to these wood strips. The only way you're gonna get these to work is to try to cut away the lathe and the plaster above the drywall around your hole, so that the light can sit down agains the drywall and the clamps will also then secure against the drywall from above.
You don't want to screw these clips through the inside of the can or mount them any other way than what they're approved for. You also need to make sure that the ones you bought are IC rated if they'll be in contact with any insulation or wood.
Home Depot sells Halo brand recessed lighting and they are of great quality. Here's a link that'll show you what their 5" IC rated can looks like and you'll notice the clips are secured from above and are basically a pressure clip that pulls tight to the drywall.
http://www.homedepot.com/prel80/HDUS...-D27X-_-325947
Your only other alternative would be to patch your holes back up and install some track lighting.