This is what I did:
1. Downloaded SkyUI 2.2 from the Nexus.
2. Did https://www.reddit.com/r/skyrimmods/comments/5awtkm/guide_quick_and_dirty_way_to_remove_skse_warning/.
And it's working seemingly fine. I haven't tested it extensively but so far so good. So as far as I'm concerned I now have SkyUI for SE. This should at least be good enough while waiting for newer version (which might or might not come).
So basically it's https://www.youtube.com/watch?v=DB_GVg0PxCY, but without the warnings and the non-functioning search function.
I posted this over at the new beta community as well.