Threema has given me the credits to set up a Gateway account \o/ thanks folks! I will look into what kind of infrastructure is needed for an E2E account but again, I do believe it's overkill for our purpose.
It might be good to have if we ever want to use Threema messages for more advanced purposes — for example, verify non-OpenPGP keys by sending the fingerprint via message. This has the giant drawback if making this information "centralized", only Keyoxide (the project's instance) could access it, not other instances. Unless it's built into a separate public service, but that's a different discussion.