I'm pretty lazy for the most part, so I'm all about doing things the easy way. Even if you let the beer sit for a long time, you'll still get sediment in the keg. As you've found, it'll settle and you can pour clear beer, but if you move it, it'll be cloudy again. Even moving it in the kegerator stirs it up.
So, I found a super easy way to take beer to go in a keg! I bought two black quick disconnects (both for the "out" side) and about 3 feet of beerline. Put those together to make a beer line jumper cable.
My procedure is this: Make sure the first keg hasn't moved and is pouring clear beer. Sanitize a second cleaned keg, and then put some co2 in it.Turn off the gas to the first keg. Hook up the "jumper cable" to the first keg and pull the pressure relief vavle on the second keg. Hook the second black QD from the jumper cable to the "out" line of that second keg. Turn on the gas to the first keg, and pull the pressure relief valve on the second keg and the beer will flow. Keep pulling the pressure relief valve on the receiving keg so it will keep flowing.
This keg will have very little yeast still in suspension, and will pour clear after you move it. Those steps I typed up seem complicated, but this literally takes a minute to do once the jumper is made. I just sanitize the jumper line when I sanitize the keg, and I keep it on hand.