said by Dennis:
That was on my list of options but I took it off because of the 1% chance that the clog might not be in the 23' run but rather in the 5' feet of pipe that drops it down into the basement.
Vertical pipes shouldn't clog that badly. They might not be pretty, but should certainly be in better shape than horizontal runs.
What about using enzyme drain treatments for a month or so to "eat" the fat/grease ? Since you're careful about what you put down the drain, you shouldn't have to use it long-term.