Started playing my promotions, and they've gone okay so far, if way different from nearly all of my normals.
For one, my first two games had two AFKs in a row. The first time, the AFK was our jungler and I thought we were screwed, but we played confidently anyway, won every lane, pushed every objective hard, won all the teamfights and won the game at around 25 minutes before their number advantage could come into play. The next time, our AFK was the midlaner. So I was winning more or less winning top lane with Karthus against Zac, but the enemy Zed was getting free farm for days in midlane while periodically roaming to 3/4v2 our botlaners who weren't doing so hot. Our jungler was counterjungled hard thanks to Zed's support, and in turn I soon had their jungler camping my lane since I was the only one doing well. Our mid laner returned about 5 minutes after we lost our first inhib, but it was way too late by that point.
I then won my next three games in hilariously similar fashion; in each game I ended up playing mid lane Malzahar, in each game my lane opponent was probably the most capable on the enemy team, I fell behind initially due to ganks and then caught up mid/late game, and all games I went 6/3 K/D with my A being 6, 9, 10 and my CS being approximately 125 with all games ending between 27 and 30 minutes. I found that two things made the big difference; first, I would start warding like crazy once I fell behind (in 2 of 3 games I was 1/2/1 at around 8 minutes), and then our team's newfound vision would allow for massive map control and for one person on the team to get really fed by catching people out of position. At this point, while we might be close in kills, we had complete objective control, a massive gold advantage, and at least one very fed team member capable of squishing people (that I could peel effectively for with my ult), and it was a complete stomp.
So I guess the moral of the story is that winning in (promotional) ranked isn't necessarily about focusing on hypercarrying so much as it is setting up the team with vision and getting into situations where you can have a slight early game disadvantage in kills in exchange for superior map and objective control. Of course, this won't work if your team is completely incompetent and is feeding hard (though from what I've tried, positive encouragement + advice can reduce feeding to some degree), but it's a lot easier and more straightforward than hoping you get a matchup in which you can decidedly carry the entire team on your back without getting focused hard by the enemy jungler.