This would be a great use case of SSH over HTTP/3[0]. Sadly it doesn't seem to have gained traction.
[0]: https://www.ietf.org/archive/id/draft-michel-ssh3-00.html
[0]: https://www.ietf.org/archive/id/draft-michel-ssh3-00.html
I also know how to use SRV records so this is a non-issue for me and everyone I work with.