Turns out PaperMC patched this themselves here: https://github.com/PaperMC/Paper/blob/1.18.2/patches/server/0870-Fix-save-problems-on-shutdown.patch
I've confirmed that this does fix it by testing with and without the patch.
This patch (or something similar) should be applied upstream.
IAmLiterallyABee
Turns out PaperMC patched this themselves here: https://github.com/PaperMC/Paper/blob/1.18.2/patches/server/0870-Fix-save-problems-on-shutdown.patch
I've confirmed that this does fix it by testing with and without the patch.
This patch (or something similar) should be applied upstream.