I did a fair bit of background/framing research into this topic a few years ago. My conclusion at the time was that the most interesting and viable path forward was to port KVM to run on top of Genode, and then to port Qubes to use that.
I haven’t re-examined the topic in recent years, but Genode has continued to flourish and is an active project with sound design decisions; using it would enable using highly secure microkernels as the basis for Qubes. KVM is mostly interesting because it is the most modular of the production-grade, featureful hypervisors that see widespread use in industry.
I have not started working on it. I am willing to and interested, but since it’s a very big project, it’s something I’ll only start if there are others interested in collaborating. (Note, I do not have deep skills in this type of programming, but I’m willing to learn as I go.)
The Genode project itself has expressed interest in both KVM and Qubes, it’s been on their “challenges” page for several years, but as far as I can tell, no movement has been made on it: Genode - Future Challenges of the Genode project
My conclusion a few years ago was that e.g. seL4+Genode+KVM was the most promising path. I’m not tightly attached to that decision, though – if others have different opinion, I’ll follow wherever the logic (given a certain set of priorities) leads.