But it doesn't seem like it's intended to be used by developers and could change without notice. What solutions are people finding the most success with? Are there any plans to have better support for this in the near future?
I think the __st.cid is a good solution.
If you want to make sure the logged customers data is correct. You can use the ScriptTag API to achieve.
1. Add a script resource to store via ScriptTag API
2. In the script use the __st.cid to get the current customer's ID
3. Save the result from the step.2 in browser's localstorage and your app can access it
Does it work for you?