Couple quick questions: Can I run the Stellarmate OS on a NanoPC-T4? If so, any potential problems? It seems to me for a little bit more money, the Nano would give me a nice bump up in performance and stability vs. a Rpi 3. Yes - No?

Thanks in advance for any info anyone can share!

The Stellarmate OS won't boot on the NanoPC-T4. If you know how to manipulate the boot files you could probably make it work. I don't know how so I moved on to the FriendlyArm OS'es that you can download from their website:
wiki.friendlyarm.com/wiki/index.php/NanoPC-T4#Get_Started
Of course they are not plug and play for astrophotography, you will need to setup Kstars, astrometry, hotspot, etc . If you don't mind putting in some work its not really that daunting, just takes some time figuring things out.
I ended up using an Armbian image which FriendlyArm also makes available for download on their website. You need to install all the astro stuff same as the other OS'es but it is pretty easy and the system runs very well.
As far as performance, the NanoPC-T4 is a significant step up from my Raspberry pi 3B, really no contest.
Another plus for the T4 is it can accept an M.2 SSD drive. I have a 240G on mine which costs around $60. With my camera plugged into the T4 USB 3.0 port saving image files to the SSD is almost instantaneous.

Do you know if Astroberry stack (which uses Ubuntu) would run on the NanoPC-T4? I'm not a Linux guy, so I would prefer avoiding building the OS and software stack from scratch. If not, what other more powerful, low-cost boards (SBCs) can run Stellarmate?

I'm pretty sure both Stellarmate and Astroberry are Raspberry Pi specific. Maybe the authors can confirm? I tried Stellarmate on the T4 but no go, I suspect Astroberry would be the same but I haven't tried.
I don't know of any SBC's other than Raspberry PI that will work.