Surprised at so many of these answers. We own at BLT and have rode this so many times, I used to time it but I no longer do so don't have my actual numbers. I always consider BLT close to two parks (timewise), MK and EPCOT.
The monorail to TTC is about 4 minutes (whole resort loop is about 20 minutes) and it's rare that we've waited more than a couple of minutes, this includes Christmas. Loading time is extremely fast, not like the busses, since ECVs, strollers just roll right on and every car has a double opening to load (none of the single file in the front door of the bus). Down one very short ramp and up the other, wait a couple of minutes. Monorail to EPCOT I believe is about 8 minutes and is wonderful. It loops over Future World and around Spaceship Earth giving you a birds eye view of the park, just a wonderful way to start the day! So twelve minutes of riding and perhaps 10 minutes of walking/waiting.
Coming back after Illuminations will mean you are in a lineup unless you are walking home so it will take longer but much faster than bussing and the resort loop will be 16 minutes instead of 4 minutes since it only goes one direction. We often walk to Poly for a Dole Whip or take the boat to MK and walk home, it's never felt like a burden. If you have tired kids, you can always Uber back.
The extra security is the monorail security at the Contemporary, there are usually two lines, fast line and bag line. We travel light, throw our phones in the security bucket, walk through detector, pick up phones and off we go!