The job of the GTM is the monitor the LTM and the LTM monitors the application instance. So, in your scenario, are you saying that the application fails, LTM notices, tells the GTM, then the GTM starts handing out the new available site, then the client fails because it never re-requests? If so, getting GTM to hand out the IP address of the broken application won't fix this will it? You application is down and the user's requests would fail anyway.
(If you want to do this, you don't need a wideip in GTM, you can just add a host A record) in Zonerunner since it is static, there's nothing dynamic about it. GTM will only hand out IP addresses that it sees as UP if they are defined in a wideip). The only static IP in a wideip would be the Fallback IP. You can select this as a fallback DNS response in the 3rd load balancing method)
In versions 9.2.X and later a feature called Route Health Injection was introduced. This allows the BIG-IP to participate in BGP, OSPF, or RIP to pull virtual servers in and out of dynamic routing so that IP address would move over to the second site and be hosted by your LTM's at site B. You'd need to run that same routing protocol on your routers and make sure to have the routing module on your BIG-IP LTM's.