Okay, so after wrestling with the clips for 30 minutes, I abandoned the idea of using them. Here's what I did instead- I went down to the hardware store and bought a pack of "Decker's hump Hill's Pig Rings" (copper coated hog rings), and double hog ringed everything- I used one hog ring as an anchor to the spring, then hog ringed the doubled-over vinyl seat cover into the anchor hog ring. See pics. Worked great. Doing it this way, I had enough fabric to double it over when I put the ring through.
doing it this way probably does't make much sense at first glance, but the size and orientation of the of the spring plate holes made it really difficult to get a hog ring into them while stretching the fabric at the same time- this made doing that a little easier. And I used a LOT of hog rings...
Using an anchor hog ring system {Edit- I added the wrong link- fixed now}