Getting the last few renowns is slow going for me as well.
It does seem as if the "Support colonization efforts" mission pops up more frequently. I've had 3 of those crit already, so at this rate I'll have got all the available purples before I achieve the remaining renowns! I'm also swimming in refugees.
So I have to check every 20 hours? Since past chain 3 they no longer show up in the sector list?
I have had no problem locating 4-6 in sector space. I think the increased frequency of 1-3 has given some players the impression that the next mission should always be available at completion of the previous assignment. I understand the permanent availability of 1/7 and the commonly available 2/7, but around 3 it should be slowed down a bit.
Also, it has been my impression that the Colonization Chains are primarily sector assignments with a secondary dice roll to access them through the bridge officers. If I am wrong about that, that could explain a lot on why we aren't hearing of the 7s even when they are available.
2. As more and more users finish it, they no longer see it. I say at the HC for 2 hours the other day asking to be invited to anyone and everyone's ship that passed by. Out of 20 or so invites, no Ops had it. Kind of ridiculous for a mission that according to the sheet is common (Only assuming that due to its in white text and other rarities have there respective colors).