Call Harry!
I recently rebuilt an old Omega DII. In the process, I got with Harry Taylor at Classic Enlargers and learned just about everything there was to learn about them. There is an excellent Q&A forum at
www.classic-enlargers.com.
I have both the 135 and 150mm lenses on the appropriate cones. I haven't measured them but I believe they are 2-3/4" and 4-1/2" respectively. I got the 2-3/4" cone on E-bay for $20.00.
Both lenses have their uses and other than circle of coverage, I don't see much difference in image quality between the 135mm Nikkor and the 150mm Schneider. I haven't printed anything bigger than 16X20 so I can't speak directly to coverage for prints above that size.
However, e-mail or call Harry - I don't think anyone on the planet knows more about those old Omegas.
Wayne