Multiple autopilot profiles in TS for existing devices

Autopilot will not (automatically) work in pre-imaged environments. Autopilot is performed during deployment, and a pre-imaged device has already passed that stage (as explained in: https://docs.microsoft.com/en-us/mem/autopilot/deployment-process). This also explains why you have to use "Reset my PC": this will return the device to the the deployment stage. 

Downloading and copying the JSON-file to %SYSTEMROOT%\Provisioning\Autopilot (for example in an MDT task sequence) is indeed an option. A good (albeit older) blog post about this is https://osddeployment.dk/2018/12/08/how-to-deploy-autopilot-device-fast-with-mdt/. 

A device can only have one Autopilot-profile assigned.

The Group Tag > Dynamic Group > Autopilot Profile process you describe is correct (and something I personally use a lot) but keep in mind that this has nothing to do with "enrollment" (I assume you mean Intune enrollment). It will not be applied during MDM enrollment, you will still need to "Reset" first. 

If you are injecting profiles into an image, you could create different images/task sequences for each profile. For your business case I would suggest using language packs instead, but that's just my preference. 

Finally, you do not have to install multiple connectors (although that might be a wise thing to do). Your service account of course has to have the correct permissions (like manage devices in all domains) as described inhttps://docs.microsoft.com/en-us/mem/autopilot/windows-autopilot-hybrid#before-you-begin.