Okay, you've come to the right place! I've got two Fila Brasileiros (Brazillian Mastiffs) and a German Shepherd/wolf mix. This is going to sound awful to people who've never dealt with these dogs, but trust me, I KNOW what I'm talking about here!
I seriously doubt, with those dogs, that an electric fence for dogs will have any effect other than a pleasant tickling sensation. You'll need to go to a farmers' co-op or other agricultural supply store and get an electric fencer - yep, the one we use for cows. The good news is now you can get a solar powered one! Run your wires on posts - and this part is very important (I'm also a paralegal) - about a foot INSIDE your boundary fence so that someone would have to be reaching into your yard to get shocked. You'll need to get tall fence posts because you need to have the top wire high enough that your escapees get zapped the first time either one of them tries to make the jump. You can run a second wire down a little lower, below the top of your existing fence line.
Be prepared. The first time they get stung they're going to yelp like someone's killing them by inches. It hurts, but not as much as they play it! I know. I've been in a few fences!
Before anyone starts yelling about cruelty, these are very large dogs, and the Mastiff breeds typically have an extremely high pain tolerance, so it takes something real to get their attention. It doesn't damage them, and they learn to "smell" the electric charge on the fence and stay away from it , usually after their first encounter, although my youngest Fila, Kharma, was quite affronted the first time she got stung when she was 10 weeks old and turned around and bit the fence - twice! And you've got to remember that the momentary pain of the shock is infinitely kinder than having dogs end up being blamed for every bit of mischief that goes on, the owner being sued because someone got scared, or something worse happens, whether it's the dog's fault or not. When you've got big dogs like these, everything gets blamed on them, and that blame too often ends up with the dogs being taken and destroyed.