It seems like all of these little Ninjas have the clutch perch with the mirror mount hole. Maybe even on the bigger bikes too. You can see the plug in the hole on my 400 below.
It doesn't specifically help you guys, but here are pics of my bikes' setups. It at least might give you some ideas of things to try.
The Ram steering stem mount just happened to use the same size screw as the gauge cluster trim on the 500. I took out the rubber part and screwed it in above my gauges. Gave a nice mounting point up under the windscreen.
On the 400, I used the stem mount as intended.
The end of the arm nestled into the curve of the handlebar bracket well, and the
Finger-Grip did a great job of holding a bunch of different iPhone models over the years. The screen was easy to see, but it was still basically right over the top of the fork tube, so fairly protected by the fairing in front and various hard parts around it. With a magnetic Qi charger on it and hardwired to the accessory power, my phone started charging as soon as I dropped it in when starting the bike.
However, I like my new setup best of all.
https://www.ninjette.org/forums/showthread.php?t=397002
Bigger screen, better interface, and my phone stays in my pocket. The downside is that the phone isn't charging, but it also uses a lot less battery when the screen isn't on.
On my buddy's VFR, he was able to use the top part of a handlebar U-bolt Ram mount with some longer bolts on the front two gas tank mounting holes, right behind the steering stem. It basically ends up being the same location as a steering stem mount, but bolted to the frame. I don't think any of the little Ninjas use tank mounting setups like that, but one more idea you might be able to turn into something useful.