MicrosoftJohn_Kelbley and I have discussed this topic frequently with cross cloud scenarios being pretty common now days. I've actually created a Host Pool Deployment solution that will accomplish this by selecting "Alternate Tenant" and pasting in the Host Pool Registration token from the other Tenant / Cloud. It will then use the same extension and pass in the provided token and register it to the "alternate" tenant or cloud. You can also pull the ARM template and UI Definition, modify them to your liking and create independent Template Specs within your subscription(s). Otherwise, you can simply click the appropriate blue button for deployment. This prevents the need to have a separate temporary host pool that you then have to run a PowerShell script to unregister and re-register.
https://github.com/JCoreMS/HostPoolDeployment
