...interesting you use the AM 120 Nikkor, aside from price and rarity is there a reason for that over say a 150 Apo N?...
I don't have an Apo Rodagon N enlarging lens, but, even if I did, it's optimized for 6X magnification and specified as usable down to 2X. At 1.5X, the 120 Nikkor AM-ED, which is an 8-element macro lens optimized for 1X, performs superbly. It doesn't have enough coverage for much larger prints than, say, whole plate size from 4x5 negatives, but I don't think anything can beat it at 1.5X. I doubt I'll ever encounter a 170mm Apo El-Nikkor, which was optimized for 2X from 4x5 and is extraordinarily rare, but suspect the 120mm AM-ED is just as well corrected for 1.5X. I did buy a misrepresented ("brand new") 180mm Apo Nikkor to try for 4x5 enlarging, but its rear element was badly scratched and I returned it to the eBay seller for a full refund, including shipping both ways.
...you are saying the 135 N is sharper than the S and not the other way around? I have heard it is in the center but not sure at what distance...
Yes, my N is sharper throughout the 4x5 field. My scene places most objects, including the resolution chart, 50 feet away. The N series was computed for 1:20, while the S was designed for 1:10. While the S might maintain its central sharpness further out from the center, it never reaches the N's sharpness under these conditions. I had the film oriented vertically and around 14mm or front rise when making this comparison of the 135s.
...Now I am wondering how it compares at or near infinity because that is how I mostly use the 350...
My back yard isn't that big so I settle on 50 feet as the best available test simulation of infinity.

I don't think the sharpness ranking of 350mm Apo Tele Xenar and 360mm would change at infinity, but testing them would be the only way to know for sure. Also, always be aware that sample variation can be significant enough to change results.