How to track UASF support? It's easy to see that currently 50% of the hashrate supports Segwit.

It's also simple to find that about 1000 nodes are supporting it. But I can't seem to figure out how significant that amount is, since all the total node counts are very rough estimates, and not all nodes are public.

So what is the best way to find out how solid the support under non-mining nodes is right now?
The total node count is not relevant. It's easy to spin up  nodes, or even fake nodes that just report a certain user agent string. That doesn't mean that they care about the rules, plan to keep following them if the hashrate majority goes another way, whether they'd even notice if they're forked off, or even whether they actually implement the rules.

What does matter is how much economic activity is following the fork's rules, and whether they're planning to keep doing so regardless of what happens.

Measuring that is something you cannot do inside the protocol. You need to look at company statements, press, ...