S.L.
I don't think it is much different for them to fall asleep being rocked or fall asleep at the breast. In either case, they are going to be upset when they realize they have been laid down. They were in such a warm and comfortable place, not to mention very safe and loving. My problem with allowing them to sleep like this is that it really does lead to getting nothing done around the house. I've had a lot of babies in my time as a provider as well as my own. Night isn't so bad because they are wore out by then and are not going to have the energy to fight you. Some babies don't really need as much sleep during the day. At least, they think they don't. I am afraid that sometimes all we can do during the day is let them cry it out.
My grandson, now just 2 months old today, is starting to become hopelessly spoiled in this way. His mother will not put him down during the day and when she needs to do something she just hands him off to one of us. If we put him down she will rush through whatever she was doing and sit with him again. So by the end of the day when she goes to work, he's bellowing the second I try and do anything but sit with him.
I wouldn't worry too much about the burping at 5 months. It's been my experience by then that their body will take care of that on their own. My best guess is that this is all about wanting to sleep in your arms during the day.
It really won't take many days of just making it clear it's naptime. Once you put her in that crib, don't go back, don't get her up, don't talk to her. Just let it be whatever happens. Last night I let my grandson cry it out for just a few minutes on the floor. He didn't even fall asleep. He just decided that I wasn't coming back, stopped screaming and started smiling and looking around. I had another 30 minutes or so of him being happy as a lark before he started demanding I pick him up, which I happily did at that point.
There are no easy answers with these little ones. What works today, may not work next week. The best thing you can do is stay flexible, try a few different things, pray about it, and when you decide you've tried it all, pick one and stick with it...at least for a few weeks! LOL. Then they give you something new to guess about.
Suzi