do you happen to know what further steps does the team need to take to route the application and if these are complex or how long they take on average to do the change ?
My thoughts :
This may not be too complex to route , as they must be freshly sorting on approval date each time they sit to send invitations , but
Lets say, you were 100th person in a queue in place 1, and on relocation => you moved to 150th or 50th person in place 2.
So you have to see if [ time taken to process application for 50th place + routing time ] is less than in your current 100th person in a queue in place 1.
And if you end up being 150th person in queue in place 2, then gone!
Don't move just to fasten this process, if you are not so sure and call them to route your application.