dds, what you describe is a baby who needs to be with you and is very sensitive to not being with you....I still think you need to speak to someone at length, because it's only by having someone listen and ask questions that you can get the support, and possible ideas, you need.
Some babies are, indeed, like this. For most of the human race's existence, and even now in pre-industrial societies (which still exist), this is what babies do - they are next to mum all the time day and night. We have evolved to be like this as babies. It is a natural and normal state to be in - but wow....in 21st century western society it can be exhausting and demoralising to care for a baby like this. Some babies adapt pretty quickly to cots, prams and scheduled feeds. Other babies don't - and being wakeful after just a few moments of not being next to mummy is not a sign of hunger, but a sign of sensitivity and awareness, and a very strong preference for the favourite place to be. Your baby's weight gain is slow, but not alarmingly so, and it may be that going with the flow and not taking her off or expecting her to sleep away from you could boost it. OTOH maybe this is physiologically normal for her, and you are already doing the go-with-the-flow thing.
Babies who are given the comfort and response they 'ask' for when small are less likely to be miserable and whiny later on - this has just been confirmed in recent research but there are loads of other studies showing the same thing.
Whatever....you need support and help to sleep. Someone needs to be able to take the baby and be prepared to hold her close while you have a break, and this needs to happen every day.
Your dd1 needs a little bit of guarenteed mummy time every day, too, without the baby being there.
The 'solutions' of formula, or expressing and adding formula to the EBM, are not really solutions, I don't think, at least not for somone who is very keen to bf, as you are.
In time, my guess is this phase will pass and your will find bf is a breeze and a great way of feeding conveniently.