Olivia was very similar to this. For the first 4 months. Then she was a legend sleeper. But for hte first 4 months it was chaos. I attempted to feed play sleep, but she would only sleep up right on me.........(in hindsight I think I needed to let her get a lot more wind up......)

My advice may not be new, but I would do everything you are doing, BUT, after you have fed her, then keep her up right for as long as possible on your shoulder/holding her on your lap. Do you have a bouncinette? I used one of these a lot with Charlie and Lexie.....feed, then bouncinette as it was "upright" as they "played". Then wrapped at the first tired sign and into bed......

That said, we used a hammock, which helped heaps.......an Amby one. Worth looking into.........

Good luck!