From about between 3,500-4,500rpm at about 1/8 twist of the throttle I'll get a miss/stumble/stammer. Happens with the engine cold or hot. Harder acceleration through 3,500-4,500rpms it's not noticeable. It's a minor thing, but there. I ran the bike over 1,000 miles this past summer like this with no issues, but I've started tearing into a few things and thought I'd address this.

The bike sat for 27 years with gas in the bowl; nasty! I bought a carb rebuild kit from Niche Cycle on eBay shortly after bringing her home. I disassembled the carb and cleaned it in my ultrasonic cleaner and installed all the new parts plus a new o-ring at the bottom of the main nozzle. Well, I didn't get the main nozzle out, couldn't figure it out, but everything else was out and cleaned. I also blew carb cleaner through every orifice.

Yesterday I pulled the carb and took it apart to look things over a bit better. This time I was able to get the main nozzle out and blew carb cleaner through it, seems fine. The pilot jet from Niche is the correct Mikuni #30, however the main jet appears to be an off brand, but is the correct #160. The carb's original Mikuni #160 is clean with no obstructions, so I put it back in. The Niche supplied needle clip is situated in the correct third grove down from the top and the air screw is turned 1 1/4 turns out. 

The only obvious thing to me was some rust and pitting on the banjo bolt for the main jet. The pic I took yesterday after running it across my wire wheel to get the rust off.
 

Could this cause my issue, or does anyone have any other thoughts?

I'd be replacing the Needle Jet , and the Needle . They do wear from years of throttle use .
OEM parts are still able to be found .

Throttle position tells you what circuit in carb is primarily working at the time.  See Mikuni VM tuning manual in Tech Library to understand carb operation.  (Hint: it's not the main jet circuit at 1/8 throttle opening)

Do you have an original Mikuni Needle in the throttle slide?  Hard to tell from your description. 

Swoop has good advice. 

Gotta get that needle jet out one way or other as crud builds up around the outside & looking at corrosion on your main jet holder i think you'll find crud galore. Drive it out with a 5mm long screw screwed in until it's tight-ish as there's a thread variation between the two but that's how i do it. Also align the pin at the base when pulling it back down. Check the airway to that needle jet from the mouth of the carb. Can't remember if very small on those--don't think so--easily blocked if small & mucks up carburation through the range. I guess you had the pilot jet out & probed it & followed its feed up into the venturi & there's angled outlet hole too. Actual i think that's the idle outlet on an angle & straight up from pilot is the--'what do they call it'--compensating hole--'progression hole' that's it. Or put a 360 carb on like i did--sorry ignore that lol.

The needle jet, or main nozzle as Partzilla identifies it, or emulsion tube as my neighbor calls it was removed and blown clear with carb cleaner yesterday. It and the port in the carb it passes through appeared clean when I had it apart.

The needle is new and came in the rebuild kit from Niche Cycle. I don't know if it's Mikuni as the pilot jet is or an off brand as the main jet was.

I received the bike with only 2,100 miles on it, so it didn't have wear from years of throttle use.

There's no crud anywhere in the carb, it's spotlessly clean. Ultrasonic cleaning (several times) and then ran a tiny brush through every port and orifice. Then blew it all through with carb cleaner.

The pilot jet was removed to be cleaned and replaced with a #30 Mikuni and carb cleaner blown through.

I was thinking along the lines of what Mark stated that it may be a transition point where different jets are coming into and out of play. I'll download the carb tuning manual.

Kit slide needles and jets are usually aftermarket and often cause issues. They sometimes have same sizes stamped on them but may not be calibrated the same. Try installing the original Mikuni needle in the throttle slide.

If you don't have original needle, you could try moving clip down a groove on needle to 4th from top (raises the needle) you have and see if problem is worse or better.  I suspect it will be worse.  Then maybe try second groove from top which is leaner...  but be careful going leaner.

I still have the original, correct, Mikuni 5DP7 needle and it looks in really nice shape - I'll reinstall it. The needle from the Niche Cycle kit looks to be stamped Y19A.