Hi Blair,
you are not able to move a subscription for this purpose into another tenant - using lighthouse the delegated resources (Subscriptions, Resource Groups) will stay in the original tenant. Otherwise, there will be a big trouble around the Identity and Access Management.
The other important aspect is, that the managed subscription oder resource group is also in a context of any cloud governance at the customer tenant - so all policies from the original would not be able to work anymore if you move them.
What you as a CSP can do - during the onboarding of the subscription you should deploy the policies to the customer tenant and then assign the in the customer tenant using any infra as code solution. You can look at our enterprise scale reference implementation, where we use a pipeline with "azops" to assign policies to different scopes.
I hope this helps to get into the right direction.
Best
Niels