The better and more expensive line of Nikon process lenses were the symmetrical 4-element dialyte type. I have a set of those. But they also offered less expensive process lens options, including wider angle for sake of small "stat cameras". Nikkor Q implies a tessar. I've only tested the dialyte category I actually have, which were the predominant lens choice in high-end print shops here on the W Coast, and preferred by certain big photo labs too for enlarging purposes.
In terms of potential camera applications, I mounted some of these on Sinar lensboard to make comparisons with my regular view camera lenses of comparable focal length. Since I own some especially good regular lenses from series like Fujinon A, Schneider G-Claron, Kern Dagor, and Nikkor M. The Nikon dialyte lenses were superior to all of them in terms of sharpness, apochromaticity, and extreme range of near to far usage. The downside is the lack of built-in shutter, smaller image circle than my plasmats (GC, Fuji A, misc general purpsose plasmats) or my Fuji C lenses, and a rather annoying double-lined out of focus rendering (bokeh) if that kind of photography were in mind.
Since I use several of these - the 240/9 and 305/9 quite a bit in the darkroom, it's easy to compare the results there to my regular enlarging lenses, including the excellent Apo Rodagon N's. There too, the Apo Nikkors excel.
Note that the shortest Apo Nikkor which exists is the 180/9 - hard to find, but they do sometimes turn up. Shorter than that, then they made the 105/5.6 Apo El Nikkor, no doubt far over your budget and possibly too heavy for your Beseler lens mount to reliably support. It would be ridiculous overkill for the projects you have in mind, Sureshot. For awhile, Apo El Nikkors were sought out for high end scanning back applications, like repro-worthy copying of paintings. But the preferred equipment has since changed and become more specialized overall.