I'm hoping to do similar myself. Tapping a finished brew off into a fresh clean keg, leaving the sediment behind in the brew keg should also allow it to travel better and not shake the sediment back into the beer.
My thoughts are:
Close the pinch valve, remove the dispensing tube from the tap, put the black connector off the spare dispensing tube onto the open end of the tube and connect that to the dispensing outlet of the spare keg. This may need a new longer tube - maybe not. Not sure yet.
Open the pinch valve slowly and let the beer flow to the new keg under its own pressure, then use the CO2 pump to push the rest of the beer through, carefully leaving the sediment in the bottom. This should disperse all the air in the new keg and leave only beer and CO2 so no oxygen is in there to start affecting the beer.
Close the pinch valve, remove the dispensing tube from the original brew keg and remove the black connector, fitting this back on the spare dispensing tube ready to use on your next brew once you've cleaned the original brew keg. You then attach the CO2 line and pressurise the beer a little in the new keg to keep it fresh.
You could then leave the freshly kegged beer in the fridge while you brew another batch in your spare keg, continuing with the above procedure to fill as many spare kegs as you've purchased.
Once you've transported all your kegs of glorious beer to your new drinking locaiton, put a keg in machine, hook up CO2 and let it repressurise.
Once the equal pressure transfer kit and spare bottles are available from iGulu, it should be much easier to transfer beers to take away and sample with your friends but that's never going to be as spectacular as showing up with the F1 machine and pouring everyone one of your famous brews straight from the tap.
This is still all theory as I've not recieved any brew kits or spare kegs yet. I just have a black F1 sat there waiting to be used. I do have a UPS tracking number now and have kits and kegs in transit, heopfully arriving on Monday