Discussion: Isolate the Problem
“...[Y]ou discern there is a problem. Now what? Uncover the precise problem.”
By eliminating systemd from the possible causes of the problem you can 'see' the remaining possible causes.
Your point is quite well-taken, of course. And you're quite correct in assessing that systemd is indeed a very likely culprit, and that deploying sysV would therefore likely fix the problem. The larger issue for this OP is that any systematic approach focused on finding a solution might actually succeed; consider one viable alternative...
1) Look for a relevant systemd bug (ideally, Jessie-specific, since Stretch supposedly doesn't have the problem):https://lmsptfy.com/?q=systemd%20shutdo ... debian.org
2) Sure enough, there are perhaps as many as 100. Click on the first link:https://bugs.debian.org/cgi-bin/bugrepo ... bug=788303
3) Wow. Sure sounds potentially pertinent. Is the bug fixed?
4) According to the bug report, yes, the bug is fixed. Is that fix available in jessie-backports?
6) Consider applying fix, instead of merely bemoaning the problem (or raising obviously irrelevant issues such as video drivers
7) Repeat as necessary. Or install sysV. Or install Stretch and be done with it.
And therein lies the real issue: some folks would rather wallow in a problem than fix it.