In that case, you can skip the line cleaning completely for 2-4 batches if the most important thing to you is minimal downtime. Or maybe buy one more line than you have kegs and clean the dirty line until it pours clear after at least an hour of BLC in the line.
The line you poured beer from today is likely a dirty line. Does it really matter if you like how the beer tastes? That is a question only you can answer.
It takes 2-4 days of alkaline soaking and draining for a line to pour clear from a hoppy batch. Good beer gets poured from dirty lines globally every day.