Hi,
Usually to migrate RDS 2012 to higher version like 2016 for example is planned to keep current RDS deployment settings and configurations, but as you mentioned there will be issues caused by in-place upgrade.
So if you have enough resources(either VM or physical machines) and do not want to keep previous settings, build a RDS 2016 deployment from the scratch is the most convenient way.
Moreover, despite of RDCB and RDSH/VH, components like RD Web, RD Gateway, and the licensing server could be migrated directly.
Reference links:
Upgrade RDS Connection Broker to Windows Server 2016
https://social.technet.microsoft.com/Forums/en-US/6b387384-9be2-4e29-8c9c-2bcd2e36d243/upgrade-rds-connection-broker-to-windows-server-2016?forum=winserverTS
Migrate your Remote Desktop Services deployment to Windows Server 2016
https://video2.skills-academy.com/en-us/windows-server/remote/remote-desktop-services/migrate-rds-role-services
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Hope this helps and please help to accept as Answer if the response is useful.
Thanks,
Jenny