Bambi cuddling constantly sounds alright to me, so long as you've got other people around, so can share the cuddling. If it's just you in the house all day then it's going to be a bugger long term, because you'll never get anything done. Could you perhaps look into slings? I've got a stretchy one for newborns that I've yet to learn how to tie, because thankfully DD will sleep in her basket so long as she's got a dummy in her mouth, but for babies that don't want to be put down it can be a lifesaver. You can even go to the loo with baby attached.
If you're having no luck with the basket, is there anywhere else you can put the baby down? Just for those moments where you need to dash off and do something for two minutes? We started off with the baby always going in the carseat and she was alright with that, perhaps because she could see what was going on, and also it helps when she's being refluxy. It was in there that she figured out sleeping while not on people, and then we were able to transfer to the basket (with the aid of dummy and awesomely tight swaddle).
SoYo if she persists, I'd be inclined to try a dummy - sometimes babies just like to suck something even when they're not hungry. Of course, you'll probably got shot for even entertaining the notion if certain of the pro-breastfeeding brigade get wind of it, but it might be worth considering.
Been fairly peaceful here the past few days. The man's days off work combined with Easter mean he's been home most of the week, and he doesn't mind doing baby duties so long as he can play Skyrim in between feeds, so I've had so much sleep, it's beyond belief. Only feeding issue we're having these days is the tiny refluxy tummy that means maximum of 3oz formula per feed. Which means, er, eight feeds a day. If she needs it she needs it, but I can't wait for her to be able to manage a bit more and then sleep a bit longer!