How can be D8 sites migrated in Aegir between different installation profiles, and not only between platforms using the same installation profile?

There is a solution in Aegir for D6->D7 and D7->D7 migrations, documented here, but it does not work for D8->D8 migrations.

For D8 sites, the new platform appears as an option in the migrate form, but Aegir is still looking for the old profile in the new platform, and migration fails.