All,
Just to add my observations. When I setup an Active/Standby 11.2.0 pair I had a "funny" with the Device Group / initial Sync, even though the initial Setup Wizard had gone through fine. As above, I had to manually remove and re-add a device to get this to work. I had another pair on 11.2.1 and I don't remember having this as an issue.
I don't like to jump straight to recommending upgrading as it should've worked but I wonder if it's worth attempting a 11.2.1 HF1 install to see if this helps. F5 Support may come back with this as an option anyway.
Alternatively, does Force to Standby on the current Active result in the Standby coming up as Active? Or rebooting / powering off the Active? If not you may get different errors which shed more light on your issue.
Looks like you're getting some good advice anyway but thought I'd share my experience too.
Hope this helps,
N