No need to shut off the CO2 when replacing a keg.
What was sticking closed on the Kiltlifter beer, the faucet? If so, I guess you have regular rear sealing faucets, not the forward sealing ones most homebrewers use.
You best strategy is to spray the inside of the faucets with some clean tap water after a day/night of tapping to rinse it out. Following up with a sanitizer will also help keep the channel inside the faucet sanitized till next use.
Sweeter and higher gravity beers (such as your Scottish Ale) tend to be more sticky, so you'd get more built-up inside.
To get a sticky faucet going again, spray/rinse/flush it out with water, let sit for some time. Repeat until it's operational again.