So is the migration something that the app on the phone could do (sort of automatically/seamlessly)? E.g. Breez wallet (@roy ;) ) could have a button in the settings - "Switch to provider ABC". You tap it, it asks "are you sure you want to migrate to another provider, this will take 5 minutes and 500 sats". And then it either does automatically send the sats from older provider to newer, or it could do something smarter - like downloading channel states, making old provider disabled and pushing those to new provider.

I'm just brainstorming - the main risk with greenlight-like setup is that the provider will block me from transacting (by e.g. going offline). So I'm trying to see what are the mitigations.