DD has just been "diagnosed" as having reflux by the HV, which prompted me to read this thread from the start (with much nodding at symptoms, and gratitude that she does at least sleep at night!)
So glad I found this thread - she is now 4mo, and vomits all the time. Well, not literally. She tends to vomit a little straight after a feed, especially if she burps, though she doesn't really get windy (BF baby). But whe isn't often happy on her back (though doesn't seem to mind lying on the changing mat 
go figure!) and apart from at night, doesn't really sleep unless she is in my arms. Even at night I cuddle her to sleep then lay her in her sleeping bag. During the day she likes being upright, preferably being held in a standing position, or being carried upright, as long as I am standing too and not sitting, which makes for a lot of physical tiredness, even though I'm not sleeping that badly. I also have a 2.5y.o DS, who gets under my feet a lot if I'm doing laps...
Since reading this thread, I basically haven't put DD down 
and have been holding her upright - she's fast asleep and has hardly throuwn up at all, which is a massive relief.
I'm also lucky that she takes a dummy. She refused at first, as she used to gag on it, but we tried a few different types and eventually she took to the Avent 0-3 month ones, though they only stay in for a few seconds. Still, it's enough to calm her down when she's screaming too much to latch on, as long as it's not pain. (If there's anyone still trying with dummies, what we did was rest it on her lip for a while and just let her lick at it, and then bit by bit she got used to having it in her mouth. It also seemed to get easier for her as she got bigger.)
Someone mentioned earlier about things being better in the mornings - I would definitely agree with that. DD is at her worst in the evenings - the other night she was quite literally screaming full bore for an hour solid, and only stopped when she wore herself out so much that she was half asleep, and I was able to get her to latch on for a feed. We have good days and bad days, but the bad ones end up with me walking circuits of the living room until past midnight, silently begging her to go to sleep. 
DP is my full time carer (I have epilepsy), but has clinical depression himself so can't cope with the stress when she is crying endlessly - he struggles with DS who obvioulsy wants more attention at times. So hard to do things with him when DD cries most of the time if she is put down. We have a sit-me-up which helps for a while, and on good days she will lie on her back chewing a toy, but a lot of the time she has to be held or she screams.
Oh god, just realised how long this post is going to be... sorry!