GTM setup with Cookie Persistence

We have an application setup where the application servers are spread across two Data Centers and the Primary DNS is from the Data Center 1. With the GTM load balancing between the two Data Centers. The GTM and the two LTMs are setup with the Round Robin Load Balancing algorithm and the LTM Persistence is set to Cookie Persistence. The scenario is when an application user logs in from either of the two Data Center using the GTM URL, all the Requests need to comeback to the same application server through out the user session. Now this is easily established when the same user login happens with the LTM URL, but when using the GTM URL a subsequent request gets routed to the second Data Center and hence kicks out the user to login again.

Are there any other ways to achieve this? The goal is to also keep the load balanced equally between the two Data Centers.