Bob Hagel probably hunted and more cougars than anyone will ever do again. In his book "Guns, Loads, & Hunting Tips" he covers most every thing mentioned to do with cougars.
He stated that he tried the 45AR with a keith type bullet, and it had inadequate penetration and shock.(P.376) He said the 357 with hard cast bullets penetrated very well, but "lacked punch."(p.378) He liked the big 44's with the keith type loads best.
He said that the 357 and keith type bullets "because of caliber and bullet weight."(p.378) were the least effective of the big magnums for big game.
I suggest that you check out "Old Bob." I think that he'd say that you folks with little pea shooters didn't like your dogs: or respect your game enough to kill it well.
