My experience with template routing has taught me a couple things... you need a good quality bit as the better bits are balanced dead on and thus are less prone to vibrate ever so slightly and catch the wood and dig in. For that same reason when template routing your bit needs to be super sharp so it slices instead of hacks (which then can catch the wood). I definitely notice a difference between the standard economy grade carbide bits and the (usually around 50% more expensive) better bits like the Katana brand from MLCS. The better bits are made of finer grade carbide and thus they are sharper and stay sharper longer. If you look at the cutting edge of one with a 10x lens, you can actually see that it is finer grade and has a sharper edge. This is one of those places where you kinda do get what you pay for. I say kinda because I've seen brands like some of the Bosch bits that although are pricier than the catalog economy bits, are the same bit, same grade of cheaper carbide. You pay for the Bosch name but don't necessarily get a bit that is as good as other higher end bits like Katana. At any rate, although higher end router bits do cost more initially, since they last longer and perform better with cleaner cuts and less burning, I think they are cheaper in the long run. Then for only $15 I send them to Forrest and have them professionally resharpened and they are good to go again.
Another way to keep that bit from grabbing the wood is to use a solid carbide spiral flush trim bit like this one...
Pricey, the half inch one I'm showing here which will cut up to 1 1/4 height runs around $60-70. But they last a long time and since they are shearing the wood in a spiral fashion they don't catch as easily going across the grain like a standard trim router template bit does. Downside is they do take a little more force to run the wood past them, but not a big deal. I run a lot of 1 1/8 inch thick oak and cherry making the handles of bread boards on a jig in the router table using this bit with very good results.
Didn't mean to hijack your thread, you make a beautiful folding chair as I said earlier, but thought I'd share my experience with router bits and grabbing wood since it was brought up.