Well, I kinda sat back and watched this thread unfold for a bit. You have gotten some great advise so far. I've only encountered big cats a few times in my hunting career. Never hunted them (don't eat them but I've been told they are actually good eating). But I grew up black and brown bear hunting. Blackies I have no worries about whatsoever. I'm bigger than most of them

and the ones I've encountered in camp were easily scared off with me standing tall and shouting and clapping. At well over 6 feet and a good bit over 250 I probably represented a bit too much trouble for them. Momma bears with cubs trailing encountered in the woods are a 100% total different story. Dem girls aint sceert of nuttin! In my experience with bears, I have found dogs to be about the best defense one can have next to a good firearm and knowledge of using it. You mentioned Mastiffs being too lethargic? Did you know that that breed was actually designed as a war dog? They may look a bit on the lazy side but a well trained and in shape Mastiff would tear and average blackie up. I really don't know that much about cougars but I would imagine one wouldn't want to tangle with a Mastiff either. My Rotties go just about everywhere I go (they stay in camp when I'm out hunting) but I really have no worries of anything 2 legged or 4 legged getting through them without one hell of a fight.
BTW, I saw someone mentioned blackies getting to 700 pounds? Maybe in the Zoo or up in Canada one MIGHT reach that but that is HIGHLY irregular. Average weight on blackies is around 300-400 on a nice Boar. Maybe stretching to 500 in a really good feeding area.