Honestly if all ASMs involved are running 11.x code and it is the cookie from the other device, then I am not sure why this would happen. I have seen this in mixed code environment where someone is going through an 10.x ASM and then get LBed to an 11.x ASM and the 11.x device does not like the TS cookie from the 10.x device. I saw this in my test environment when I upgraded but I managed the prod rollout accordingly and I LB between 2 standalone ASMs that both run 11.x and that works just fine.
Do you have a support case open yet?