You're going to have trouble discussing this with folks who have solved the problem before you !
It is difficult to integrate the published specifications (which try to predict) with experience (which tries to describe). An Apo Rodagon N manages to make the transition from 15x to 20x far better than do older lenses. A perfectly flat field across a 16x20 or cropped 16x20 is hard to do. Thirty years ago a friend showed me a quick way to get the best corners I could get from a given lens in a big enlargement: lay a mirror in the corner of the image, and stop down the lens until I saw a clear, round aperture.
I'd look at the best lens you have for 16x, and see if you have stopped down far enough to get past mechanical vignetting. If not,
you simply have to try a new lens. I use a Apo Rodagon N, which I got to print a show of 20x enlargements 20 years ago. It was better at 20 x than my Apo Rodagon, which was better at 15x than was my Focotar. I think it is safe to say that you can improve over the good old lenses you've mentioned in your post.
Sorry to say I have no experience with the Apo 40 or 45. Their MTF (at 10 x !) shows the need to stop down to f/8. I have no evidence to show they would match a Rodagon N at 20x, I doubt they would. All you can do is to get one in, try it, and send it back for a 50 if it doesn't.
Just another note. You're doing pretty difficult work here, and you'll need to do all the old tricks to tune your enlarger. Don't forget to align the corners of your easel. And if you are looking to go larger than 20x, look at a Rodagon G or perhaps intenegatives and Apo El Nikkors.
I use the 45 APO and also have a Rodagon APO 50 N. At 8X10 and larger, I can see the difference with these and their counterpart Comp S and Rodagon 50..... Frankly, I can't see the difference between the two APO's. As mentioned, alignment issues become critical at these magnifications/open apertures and will likely account for more image degradation than subtle lens variations. If my 45 has a sweet spot, mine shows ƒ6.3 (also a decent compromise for exposure times and some depth of field forgiveness and edge sharpness) and the Rodagon is similar. I very seldom go so large with 35mm as you are dealing with and do 35 work on a 23CII with dichro head and have not had light fall-off trouble with this combo. I gave in to a Versalab a few years back and this has made everything so easy and accurate to keep tuned correctly. I would encourage considering one and wish someone would have prodded me a bit earlier in my darkroom escapades.
I do use the Versalab, level absolutely everything (incl the easel of course) and will hopefully be getting my hands on a 60mm lens to see if there is any change. The shame is that my 105mm is so insanely sharp, but too long a FL. with grittier lower res images the 80mm is fine (not as sharp as my 105), but when the 60 or 63mm arrives it will be interesting to see what happens. I have a feeling that something is going on withs crunched up bellows or something and it is not all about the lens coverage/mag ratio. I will report back when i have tried something a touch longer than 50mm.
I use an APO componon HM 45mm f/4 to print large prints of 35mm...mostly 16x20 and 20x24. I generally try to stop down to f/5.6 if I can, but in my experience it has been wonderfully sharp straight to the corners using a glass carrier. I used to have an 105mm APO EL-Nikkor, and I sold it because I just could not see a difference in the prints between it and the schneider, and the schneider was so much easier to work with given the focal length and aperture (and lighted aperture index, stop-down lever etc).
I just won a 63 2.8 nikkor and 60 rodagon on ebay and have recently used both for 20" prints. The problem is completely solved with this slightly longer FL and I now have perfect corners that are indistinguishable from the centre. Whether it was some sort of mechanical issue, or lens curvature of field I will never know, but these longer lenses have cured the issue 100%. And the pair were far cheaper than a APO anything. Whatever the reason, that 10mm leap in FL has made the problem go away :)
Both perform stunningly well and do all i could ask so no need for any more lenses.
Glad you have found a solution to the problem :)
Interesting that the slightly longer focal length solves the corner problems.
That is worth remembering for any future plans to print large with 35mm Negs
The 45 is a wide angle design. The corner performance was abismal terrible trash on my condenser enlargers. One day when I was about to give up, I tried it on one of my diffusion enlargers. It worked beautifully. The 40 mm Leica Focotar from my V35 behaves the same way, diffusion only.
I have 4 condensers and 3 diffusion enlargers and the condensers work with nornal lenses just fine.
I can`t explain it, but I have enough systems and lenses to prove it is not a missalligned something or other.
Ronald, sometimes it all feels like alchemy! Only the other day I did three identical prints and found perfect focus slighly fell away though the three. The enlarger was locked down perfectly so who knows why, but these odd things happen! why these longer lenses work so much better I do not know, but suspect it is something to do with printing short FLs on a 10x8 enlarger. even with a recessed panel, something perhaps did not jive properly.