As long as we're only talkin coyotes, cats and grey fox, my imput is from experience (just want everyone to understand that I know what a coon looks like...and that's about it!)
Oso, the set up you describe is what I perfer. I have used the 3/32 when I first started, even have some old snares still of 3/32. I don't think it's a matter of having to go to, or should go to a smaller cable when you use tensioning locks. But rather, you can get away with the smaller cable and not concern yourself soo much with chew outs...they don't chew when they are dead. I found less refusals when I went too 5/64.
I have talked with others and the general sense of things is you will notice a bigger reduction in refusals going from 3/32 too 5/64 than you will from 5/64 too 1/16. I studied on going to 1/16 and decided that the value to be gained by "re-tooling" my set up to 1/16 cable wasn't worth the cost. Also, there seems to be more chew out problems, apparently even with tensioning locks, with the 1/16 cable (this is second hand info). The 5/64 seems to be a happy medium. I do like my snares to be at least 8 ft long...give them a good run to set the lock tight.