instanceCounterMap and Remix

Question

I'm writing an LTI in Remix and I get some hydration errors. I've implemented the InstUISettingsProvider with the instanceCounterMap. As far as I can grasp it, it lists all the components in the document and hands out an ID for them, right?
This doesn't seem to work for Remix, probably because they handle it differently than Nextjs. But I can't pinpoint where it -exactly- goes wrong. Any ideas?

When I run it without the instanceCounterMap, the ID's keep on incrementing with every refresh. How does this happen?

Maybe this question could be coupled to #1415

Code Sample

https://github.com/devinekask/remix-instructureui

excerpt from the logs:

+ id="RadioInput_1"
- id="RadioInput_0"
...
+ id="RadioInput_3"
- id="RadioInput_1"
...
+ id="RadioInput_5"
- id="RadioInput_2"

Additional Details

I also asked the Remix community about this issue.

Start with the linked remix-instructureui example and the InstUISettingsProvider instanceCounterMap behavior described in the issue. Compare the server and client ID sequences in the hydration logs; done means the Remix example hydrates without errors and component IDs remain consistent across refreshes.