Hi Leo,
You said: "When I sign into the EEM server (global) I can see the Applications "WorkloadAutomationAE" and "WCC0003" on it -- and it still has the old IP address of Server A (where WLA AE and WCC runs)."
Are you referring to the IP address under Configure -> Applications -> WorkloadAutomationAE -> Install Host Address: ?
If yes, then that is pretty much static, so do not worry about it.
"I ran as_safetool and autosys_secure on Server A and (I thought) pointed it to the EEM server but that didn't work."
What didn't work? Did you register with EEM hostname or IP?
Also, you mentioned the hostname remains the same. So long as Server A can resolve Server B's hostname, then I believe there shouldn't be any issue. Please check if the hosts file on Server A points to the correct (new) IP for Server B.
It might be worth a try, to restart WAAE and WCC services once if you haven't tried already so that the any cached DNS records are cleared. If you're on Windows try DNS flush as well. If you're on Linux, then flushing NSCD (name service cache daemon) hosts database might help. Please check with your System Admins regarding DNS flush.
Cheers,
Chandru