The Turkistan roaches are the Blatta laterialis, if I'm not mistaken. They're also called "Red Runner" roaches, because well, they run fast if they get loose.
I've never had lobster roaches to infest much, and I've had quite a few to get out due to them being able to climb glass and stick to anything. But they eventually die of dehydration after a while I've found. Always found them dead under things, or I'd see the cats crunching on one. I also tended to feed the males off and kept the females back, so never had many to get loose and give birth outside the container.
The Blaptica dubia seem pretty nice so far. They're slow, gentle, and large enough they've lost that "creepy" appearance most roaches have, and they play dead when you poke them. So far out of my dozen one has matured into a male. I can't find any information on their life cycle though, are these egg layers or live bearers?