Your expectations from systemd-sysvcompat are wrong. Do read Arch Linux wiki related section. I also think you are wrong in looking for a package to use SysVinit services. I think you should look the other way around: for a package that adopt Cisco AnyConnect, or a FOSS replacement, to systemd.
- Are you aware of Arch Linux wiki OpenConnect article? I am not familiar with OpenConnect. Since no answers were given until now, I think mentioning it is in place, despite my unfamiliarity.
- While I am at it, I think Systemd#Writing_unit_files also worth mentioning. Depending on the Cisco AnyConnect SysVInit service complexity, it might not be hard to try and write a systemd unit to support systemd. In fact, you mentioned Ubuntu and Red Hat. Don't both Ubuntu and Red Hat systemd based for several years now? Can't one adopt their systemd related unit to Arch Linux with little work?
- An AUR related AnyConnect client has its own vpnagentd.service systemd unit.
- Have you tried searching, or asking, at Arch Linux forums?
I agree my answer leaves the poster with a whole bunch of loose ends. Or even much more than loose ends. Once again, this question was left not answered at all for more then half a year. Hopefully, some pieces of information at the right direction are better than none.