High-Needs Baby: PLEASE HELP (long)

I am having a really rough time with my almost 3-month-old daughter
Charlotte. I have read The Fussy Baby Book, and I believe she is what
Dr. Sears calls a high-needs baby. Knowing that makes her a little
easier to deal with, because at least I know it's her personality, not
anything that I am doing wrong. We always respond to her cries right
away. We don't co-sleep but she sleeps in a cradle about 5 feet from
our bed. She was slow to gain weight the first two months, but then I
started supplementing with formula (first milk-based, now soy formula
on my mother's recommendation) and she is gaining about 8-10 ounces a
week now. I have been around babies a lot, (including my siblings who
are 17, 19 and 21 years younger) and I have never known a baby like
her. I have tried to describe her in detail below, in the hopes that
someone can help me.

Charlotte is:

Fussy
Even when she is not hungry, tired, or uncomfortable in any way that I
can tell, she still tends to whimper and cry. I try to make sure she
is well rested and well fed and then I try to play with her and she
usually doesn't enjoy it. It doesn't seem to be gas from what I can
tell and she's not even 3 months yet, so I don't think she could be
teething.

Drowsy but resists sleep
Tends to fall asleep while nursing, but wakes up screaming the minute
the breast is removed from her mouth. If she seems sleepy I try to get
her to settle her down for a nap and she just fusses and tugs at her
ears and hair to stay awake unless I swaddle her. To get her to fall
asleep she needs to be stuffed full of milk, swaddled tightly in a
blanket (or lying down in the sling) and bounced or rocked for 15-30
minutes. Then if I put her down in the cradle she usually wakes up and
I have to start all over again. She'll stay asleep in the sling, but
only if I keep walking or bouncing. The minute I sit down to catch my
breath, she's awake and crying.

Loud
Her cry is not the normal "Hey, I need something," cry. When she cries
you would swear someone was sticking pins in her or that she was
starving to death (even when she's just had 5 ounces of formula and
has only been asleep for 30 minutes). She doesn't whimper and then cry
and then scream if she's not tended to. She starts screaming
immediately.

High-maintenance
She always wants to be held. It is impossible, even when she is
well-fed and well-rested to put her down in a swing or bouncy seat for
more than 5 minutes at a time – if that. If I want to use the
bathroom, sometimes I can just run there and back before she starts
crying. Sometimes I just have to let her cry.

Dramatic
If the breast or bottle comes out of her mouth (through my doing or
her own) she doesn't just whimper or cry that she wants it back, she
screams bloody murder.

Demanding
If she is not being fed, she needs to not only be held, but insists on
being bounced or rocked. She hates being still. It is exhausting
constantly having to pass her back and forth with DH – and even more
exhausting when I am alone with her all day. The only option I have is
to put her in the sling and wear her all day. But I can't pump, or do
dishes or wash baby bottles or my breast pump with her in the sling,
and she only stays content in the sling if I am constantly moving. If
I sit down she wakes up and starts to cry. Plus it is summer time and
we both are dripping with sweat after a few minutes.

Insatiable
She will nurse and then take a supplemental bottle of EBM or formula
(I am having supply issues). She will act totally full. I will burp
her and then offer the bottle again. Sometimes she takes a little
more, sometimes not. She starts acting full, sleepy, and a bit fussy,
so naturally I think, "nap time" but 9 times out of 10 she's up again
in 15-20 minutes acting like it's been hours since she ate.

Unpredictable
Our days are spent in an endless circuit of breast then bottle, burp,
bounce, play (try to), change diaper, attempt a nap, nurse again,
offer bottle, try pacifier, toys, singing, shushing, swaddling, etc.
Some things will work for 5 minutes, some for 10 minutes, some not at
all. I just keep trying things until I figure out what works and then
when it stops working I try something else.

Frustrating
I get so upset sometimes because I can't make her happy and I can't
figure out what she wants. Sometimes it seems like all she wants to do
is cry. Sometimes nothing works. I try everything and then I try again
and nothing works. At those times I just put her down in her cradle
and go in the other room and scream into a pillow.

Sensitive
She loves things that are stimulating: toys, TV, the view out the
window, busy patterned fabric, etc. But after a few minutes of any of
these she becomes so overstimulated that she starts to cry. This is
partly why we spend so much time at home, because we live in NYC and
when we go out she gets so overstimulated and upset by the sounds and
sights of the neighborhood.

Intelligent
She seems very alert when she is having a rare non-fussy moment. She
has excellent hearing and eyesight, and is responsive to different
faces and voices.

Happy (when the stars are in proper alignment)
When she is happy, she has the most amazing smile. She crinkles up her
nose and sticks out her tongue and it is to die for cute.

Strong
She has excellent muscle tone now that she is gaining weight faster.
She is driven to always exercise, whether it's kicking her legs or
trying to stand.

Not Affectionate
When I was pregnant I had visions of snuggling and nursing with my
baby but she is not like that. She isn't a very good nurser, she has a
weak suck, and since we introduced bottles she has gotten even lazier
at breastfeeding. I can't just lay in the bed and snuggle with her
because she needs to always be bouncing or rocking. When she wakes up
crying from a nap it does no good to speak to her in a soothing voice
or hug her or anything. It doesn't comfort her at all. The only thing
that works is the breast, and she doesn't even nurse properly and
usually dozes off after a minute or two. When she first wakes up her
body goes stiff as a board, she screams at the top of her lungs, and
won't make eye contact. I'll put my face up to hers and say, "It's
okay, mama's here, you're okay, I've got you," etc. and she looks to
the left of my face and if I turn her she moves her eyes the other way
to look past my face to the right, but she won't look right at me.

Please help us if you can
I have been managing on 3-5 hours of sleep in each 24-hour period for
3 months now, and I am starting to go crazy. I rarely leave the house
and when I do it is usually a terrible experience. I love her to
pieces and I want to make her happy and I feel like I am failing
miserably at my job of being a mother, a role I have longed for my
whole life (I'm 31). I don't have time to do anything, I even have to
leave her crying just to wash out a bottle for her next feeding
because she won't sleep and she won't be left alone for even 5
minutes. I am worn out. I welcome any suggestions anybody has. I feel
like I've tried everything, but if anyone has had a baby like this and
has some ideas, please let me know. I just hope she doesn't have any
serious psychological or cognitive disorders that would make her act
like this. I had a perfect pregnancy and my whole family (and DH's) is
healthy and mentally stable. I have been telling DH for two months
that things will get better when she gets a little older, but she
doesn't seem to be improving. Please help us.