Don mentioned that I use the 240 with my homebrew enlarger. I actually have not used the 240 with an 8x10 negative yet, because I also have a 300 Rodagon, which I prefer for exactly the reasons you are concerned about.
I figure as long as I have the room to use the longer lens, I will use it. I don't typically crop the negs, so I can print a 20x24 on the 138 without any difficulty and the easel is not too low for comfort.
If I needed to print a smaller negative, or crop in on the 8x10, the 240 is going to be the only way to do this, because the geometry becomes difficult over about 2.5x magnification with the 300.
I asked a similar question before I built the enlarger, but I never got a suitable answer, so I just forged ahead with it, and designed it to accommodate the 300.
There is no question that the performance will be better with the 300, but the difference may be small enough that you can't really see it except at the largest size prints.
There are several issues to using a wider lens, and not all of them are tied to the optical performance of the lens. Some of them are geometry issues related to the enlarger head, which complicates the issue a bit.
At 16x20, while it may be possible to measure a difference in performance, it will probably not be noticeable on a print. At 20x24, I think the differences will start to show up. The most obvious will be the increased edge burning that you will have to use with the 240 lens. It may even be necessary to edge burn more on a 16x20.
I recommend you get a LPM swatch from Stouffer and make some tests. You would then be able to see how far the lens will enlarge before the sharpness falls off to much for your liking.
Regardless, if you have the room, the 300 is a better lens to use.