I was terrified of co-sleeping too. But in my efforts not to take DD to bed with me, I'd end up falling asleep while feeding her on the couch anyway. Plus, I was so exhausted by then that I was sleeping too deeply to be properly aware of her. It took me a while to master feeding lying down, but once we did, co-sleeping was a much better and safer option for us. The ABA website has a page on how to feed while lying down which is also appropriate for co-sleeping - pretty much how briggsy's girl described.

Have you tried keeping her upright on you for 20-30 minutes after a feed? She might have reflux which would be causing her discomfort as soon as she is laid on her back. It would also explain why she wants to feed again as feeding helps relieve it. My DD's sleep did improve once I started keeping her upright for a while after feeds. It gave time for her stomach to settle.

I also found at around 4 weeks DD just suddenly got her days and nights around the right way. She still didn't sleep through (doesn't now) but we started getting most of our sleep at night which made a big difference.