Design question #2: Active-Standby pair in two different data centers

The other option to extend L2 over L3 prior to OTV in cisco world is L2TP. While OTV helps to protect from broadcast storm going across WAN and bridging loops, L2tp might work for your case as it's a point-to-point 2DC setup. Again all depends on your full topology as in how users are connected to DR DC in the event of failure.

While OTV kind of technologies works well in DR simulated environment when both DCs are up, in the real event of PROD DC going down, consider the OTV box in Prod DC might not be available which needs to be paired with DR DC OTV.

Ideally you won't be having HA active and standby across Prod and DR(due to the above issues). Instead, IMHO, you will be having a GTM with LTM in the 2 DCs.. and GTM will do the job of directing the user traffic to appropriate LTM based on the scenario you have.