I've found problem during migration from the AD 2003 to 2016 'cause the AD forestFunctionality could not be upgraded to 2. The AD DomainFunctionality and domainControllerFunctionality are correctly at level 2.
There's no way to modify the forestFunctionality, and it's necessary to promote the Win2016 as AD Controller.
I'd check that domain functional level is at 2003 level. Also confirm health is 100% before trying.
I'd use dcdiag / repadmin tools to verify health correcting all errors found before starting. Then stand up the new 2016, patch it fully, license it, join existing domain, add active directory domain services, promote it also making it a GC (recommended), transfer FSMO roles over (optional), transfer pdc emulator role (optional), use dcdiag / repadmin tools to again verify health, when all is good you can decommission / demote old one.