I've done this mission on my main Science character ages ago, but was helping a guildie who wanted the accolade. On the last part after destroying the Iconian gateway, we were to beam up and I got the error. My guildies were able to beam back to space with no issues though.
I tried the solutions suggested here (for some reason, when I Force Verify, nothing happens), restarted the PC, and tried to do the missions twice by myself, but still getting the "Couldn't Transfer Character" error. Another guildie of mine is trying to do Cutting Accord on his Klingon, but is also stuck.
I have had the same issues on Rapier and Cold Storage. When I submitted the ticket for the Rapier issue I was told that they will look into the issue, and that I should look for a resolution on the forums.
Yet all I find here is that everyone else is having the same issue....glad I am paying for things that do not work.