bigip_add vs bigip_install vs ??

So you are correct - first check that you have a route to the LTM and that the self-IP is set to Port Lockdown -> Default. Also check the versions of big3d on both devices as these should ideally be the same (check out SOL13703) and run big3d_install if not.

Setup the datacentre and server on the GTM and run bigip_add. It should all work perfectly - they will setup an iquery session to exchange details. If not, use iqdump to check out the iquery messages.

You shouldn't have any real changes on your LTM although GTM controls monitoring to be the optimum so you can find that your actively monitoring devices can change if you have crossovers between your datacentres.