I can certainly hold my own in non-target possum catches at canine sets. Also, the first season I tried a bunch of dog proof coon traps (like Duffer's DP, Coon Cuffs, etc.) I had nearly 100% possum catch rate in tripped sets. Didn't get a coon until the final day of the season, but up to that point I was hammering the possums. It was true insult to injury for me given what I had spent on Dog Proof traps and thinking this was a way to limit my possum catches, too. Even had some pull up on the end of drowners with the darn things because the water level dropped and the possums were working my now "dry" water/coon sets guarded with those traps.
Yep, best way to catch them is to not try so hard and focus on other species about as hard as you possibly can.