Looking for solution to keep LTM HA pairs syncronized across 2 data centers.

I don't know what the functionality of the F5 Ansible module(s) is these days but this seems like a scenario where a tool like Ansible would be very useful. Of course, it won't help you with transferring the current configuration but if you deployed all further changes with Ansible (if support for everything you need exists) then there would be no need for synchronisation between devices, you would have full confidence the same change has been deployed on all devices.

Differences with IPs etc. are easily handled with variables.