Does your lens board look like this one?:
Yes, they were designed way back when Meopta enlarging lenses were quite small, and don't work with most modern lenses that I know of. I'd actually designed myself a straight-sided one, but never got around to machining it. And then I came across a cheap Beseler 23CIII, and didn't go any further with it. I think I've still got the blueprint, if you want to track down a machine shop that could make one for you, but it may well be cost prohibitive.
As far as an 80mm lens is concerned, I wouldn't think you'd have the same problem if, as you say, you'd be mounting it on the back of the cup.