I'm having the same issue. L2VPN is a solution to extend a network over the internet - fine. But, it's not the same as being able to create a universal logical router if your use case is disaster recovery. If your primary site becomes a crater, the VPN tunnel is broken and your server that is moved to the recovery site doesn't have network connectivity. I get why it doesn't work, it's just a shame there isn't a fancy way to get VXLAN traffic on ESXi hosts across networks that CAN'T have an MTU higher than 1500 to remote site ESXi hosts. NSX should have some sort of fancy packet splitter and unsplitter for just such occasions.
In the case of the OP, I think a L2 tunnel between Cisco ASA's WOULD probably work, as long as the Cisco's physical interface and the virtual tunnel interface were both set with 1600 MTU. In this case the Cisco's would be doing the fancy splitting work, right?
