Good news for you! You have slackware [0], void [1] and alpine [3], which are widely-used non-systemd distributions with sane scripts. They are well-maintained rolling releases which allow you to use much newer versions of the kernel and packages than your typical ubuntu/debian installs. I don't particularly care about systemd, but these distros are great by themselves!
Of those, I think only Void is fully rolling release; Slackware, as you note, is very much not rolling, and Alpine has regular releases and you'd have to go to the "edge" version to get rolling releases.
I've just started playing with Void because I want to use runit on both my dev machines (Linux) and servers (FreeBSD). I've really been liking it a lot, although the batteries-not-included approach did not phase me since I've been on Arch for awhile. Another thing that prompted the switch was annoying intermittent failures of systemd-resolved.
Good news for you! You have slackware [0], void [1] and alpine [3], which are widely-used non-systemd distributions with sane scripts. They are well-maintained rolling releases which allow you to use much newer versions of the kernel and packages than your typical ubuntu/debian installs. I don't particularly care about systemd, but these distros are great by themselves!
[0] http://www.slackware.com/getslack/
[1] https://voidlinux.org/
[2] https://www.alpinelinux.org/