I have to say that I feel your pain. As a public health professional, I believe that co-sleeping (which means baby sleeping in the same room as parents) was the ideal, both from a breastfeeding promotion AND a SIDS/SUID reduction standpoint. We bought an Arm's Reach Co-sleeper and were all ready to go.
Unfortunately, someone forgot to clue the baby into the benefits of this arrangement. He HATED sleeping in the same room as us, and he especially hated the cosleeper. While standard crib mattresses are hardly plush, they are softer and more supportive than the thin co-sleeper mattress. We eventually gave up on the co-sleeper and put him in his crib at night, and I nursed in the nursery.
I agree that if you aren't swaddling, that should be the first thing you try. We swaddled until 6 or 7 months-- way longer than I anticipated. If she will nap in the co-sleeper, I think you can rule that out as the source of the problem, but if she just won't sleep there anytime, you may have to accept that it isn't comfortable for her. And it may be that if she knows your so close, she's going to insist on being nearer to you.
I always hesitate to weigh into the bedshare/no bedsharing debate in a non-professional context, because people are so passionate about their positions. And obviously the majority of people who bedshare get away with it without harm to the baby. But I feel compelled to note that while people have been bedsharing for millennia, they didn't do it on 18 inch mattresses with down pillows and comforters. In nearly all cultures, men don't sleep in the same bed with lactating women. And it is only in the last 30 years that the majority of people in the culture are overweight or obese. And babies did and do die of roll over-- according to the CDC, 315 of them in 2003. I know that you didn't want to get into this, so just let me say that if you or anyone else wants access to the statistics or research on bedsharing, you or they are welcome to private message me.
Best of luck. The sleeping DOES get better, however it works out. She will start to be able to go longer and longer at night between breastfeeding sessions, and you will start to get more sleep. Just remember there are a number of perfectly reasonable ways to approach the feeding/sleeping issue, and what works for you guys (as long as it is safe) is just fine.