I futzed around with a few more tries before actually calling Google Payments support. Turns out that all transactions were declined due to a Google "security flag" on the account. The operator I spoke with said it was policy to not disclose the reason for the security flag, but the only thing I did with the account after creating it was log into Play Store on the Kindle Fire.
I suspect that this is what someone (Terry?) mentioned in another post - that the Google Play version(s) had some kind of mismatch and it flagged the device/transaction as suspicious or unsupported in a way.
The Android tablets are a bit of a mystery right now -- you have the high end (Pixelbook, Galaxy models) and the low end (Fires, generic Walmart type), but little in the middle. This may change, though, as several are set to be revealed shortly with Chrome OS and these run the Play Store / Android apps native like the Pixelbook. No word on pricing, but with brands, such as Acer, I suspect the will be middle-of-the-road.
I will say, for the most part, once you have DomoPad up and running it just runs - the processing requirements are very low outside of "has enough RAM to support your graphically intense control pages". But I have only ever had an issue with that on a 640MB device (yup, still use it as an automation controller).
Terry, why are you needing all these small tablets - I thought you had the large format tablets attached to the wall??