You're absolutely right. There are rings in the blue channel of your exposures taken with the Nikkor 55-200 lens:
Top row is your stock D5300 and bottom row is your full spectrum D5300. Camera firmware is v1.03.
That's a very useful result. Again the D5300 hardcoded correction (on both cameras!) is applied when the firmware recognises the lens but not with a telescope.
Mark
Thank you Mark! Very interesting. And though I read your website links for more details, I'm clearly still not doing the analysis part correctly. But at least I can get some faint rings to show in the worst of the files.
I haven't used lenses much of late. The last one I did, duoband of NA+Pelican, came out okay but that's a fairly bright field-filling nebula. Around the same time with the same lens, I did have difficulty with a wide-field galaxy, such that either flat field correction, gradient extraction, or both, was rendered near impossible. I gave up on that data on the assumption my lens must have been picking up stray light. I wonder now...
But, I will now follow the tips for ISO or exposure on lights and flats if using a lens.
More troubling in my case, since most of my data has been through a scope, were the colored waves. Noted by Piotr a few pages back, with him using a telescope also. If those effects are also due to hard-coded internal NEF meddling, recognizing an attached lens seems unnecessary as a trigger. They are not easy to suppress in processing either, if they even can be. One obvious example I had was of M42 with the D5300 and Newtonian, so not requiring any sort of severe stretching. One of the red stripes was baked across the top of the nebulosity. Pretty in its own way, but not exactly true color. 
If I shoot some telescope OSC with the D5300 again, hopefully the same guidance will help with the waves.