I do upholstery for a living. I have never liked point attachment where there is a large space between attachment points. I also don't like to see attachment points doing double duty.
When I did my seat, I first scraped the paint off the inner bottom edge of the seat. I marked a line around the seat bottom about 1.5" deep. Then I fitted the seat right where I wanted it, using clamps. You have to slit the fabric so take your time, tightening up until you have it right. Laundry pins are usually not strong enough. I trimmed the cover a little, but left at least 3". Then I painted contact cement on the seat bottom down to the line and on the cover down about 2.5". I do about 6" at a time, and I use 2 coats, but I'm anal. While the cement is drying on one side, you can work on the other. When you have a section done, you can cut the fabric with a carpet knife along the line since the material will not stick beyond it with contact cement on only one side. The clips now only have one thing to do, keep the trim strip on. If it comes off, who cares, just reattach or buy a new one. The seat fabric is going nowhere.
There is nothing inherently wrong with using the clips to hold the fabric and the trim strip. Bike have been built for a long time that way. Best of luck with you seat Hobot, well, not your seat, your bikes seat,...............you know what I mean.