The first thing I do is "jump" to a new keg, to leave all the sediment behind since moving the keg stirs it all up. So, before you leave, you can transfer to a new keg with a homemade "jumper cable". It's just two black disconnects, and a length of beer line. Sanitize the beerline and QDs and the new keg, and then purge the new keg. Purge the original keg (don't move it!) and reset to 4-5 psi. Put one black QD on the original keg, and then one on the receiving keg, and pull the pressure relief valve every 10 seconds or so on the receiving keg. The beer should flow nicely. Then, you have a sediment free keg to take with you.
Keep it cold until you take it on the road, and a trashcan or cooler with ice will work fine. I did that this weekend- used an Igloo cooler, and one keg and the co2 tank fit in there nicely. I took off the line, and ziptied the picnic tap line to the handle, so it was easy for people to serve.