It sounds like it does work in one direction correct? That indicates the policies are working but a configuration issue may exist.
The best course is to break out the components. Since you mentioned a standard win 7 VDI desktop is working bi-directional with the clipboard. I would login to the RDSH host directly with an identical test user. Test the clipboard and also generate via CMD a GPResult Report: GPResult /H %userprofile%\gpresults.htm.
I have Windows 2012 R2 RDSH running in my environment with Horizon 7.5.
I just testing my app and can confirm that the clipboard does work in both directions.
The RDSH server is running the 7.5 agent and my client version is currently 4.5.. its little older client. my default protocol is set to BLAST.
Have you attempted to connect to the application from the outside or a machine that is not on the domain? Where client policies would not apply? Specifically like a home PC?
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Is VMwareViewClipboard.exe running? About a month ago there was a thread that stated that "on Windows Server 2012 R2 (maybe others) the upgrade misses a couple files such as VMwareViewClipboard.exe, did a repair and everything looks fine now."
All problems were resolved by returning to version 7.4