I think this has to do with your Diplomacy rating. My Klingon told the Gorn to go to hell but I was able to convince almost everyone else to join.
My Tactical captain was able to convince everyone and only the Andorian had the diplomacy answer greyed out.
Dialog is do-able even with a low diplomatic rating... My Klingon toon was only a level 2 marauding skill, and was able to get the KDF to join in. There's just more roundabout dialog to go through. This works for all the ambassadors, and I also discovered that like most dialog dependent objectives, if you found out you screwed up when they say that in a nutshell, no they don't want to join, then just click the minus sign on the top right corner (Do NOT click continue), and then select the Borg Conference Button and you can start over again. You can keep doing this until you get they will join you and you can complete your objective. Doing this I was able to get all 4 ambassadors to join and score the accolade...
Also as for kits and abilities not being able to be used, its definitely a bug as it only affected my engineer KDF toon, not my tactical or science Fed toons, whom were able to use all of their abilities.