I completed the mission with my Federation Klingon and even got the accolade for avoiding all the Feds, but when I left to sector space the mission reset and told me to go to 23rd Century Drozana, which I do. When I got there I had start the mission from scratch. You can see I got the accolade for completion here:
I'm getting the same problem. Every time I return to the 25th century it makes me do "Shenanigans" again and I can't complete the mission. I'd really like to know what's going on and I don't want to miss out on the weekly reward.