Managed to fix this by backing out all my changes to my pre-OSOT snapshot and going through, making some conservative best-guesses on services not to disable, features not to turn off, etc. in the template.
Unfortunately due to time constraints I couldn't track this down to an individual setting or settings (needed to complete the project ASAP) but something in both the new Windows 10-2019 AND the older Win10 1809-2004/Server 2016-2019 templates breaks the vcenter/vmware tool's ability to place the unattend.xml where it needs to on the VMs.
Be cautious and manually review what settings you enable in the OSOT - even from VMware's recommended pre-checked options. Though, that's just generally good advice as the tool is kind of a shotgun - huge performance gains but some potential collateral damage.