Hello Mumma,
You are in the same position as me. Mine was born 5 1/2 weeks ago at 35+5 by section. He was in the high dependency unit on oxygen and tube fed for 2 weeks. During this time I tried to pump as much as I could but I had a shit pump (realised in hindsight) and also don't think section and being a month early is ideal for your milk coming in. I was so busy going up and down to the hospital I was lucky if I pumped 6x a day, and I started sleeping through the nights because I was so exhausted after the surgery.
I tried to EBF using nipple shields at the hospital but he started losing weight, stopped pooing and wouldn't sleep and just screamed all the time. I started topping up with formula, at first just at night. I tried to cut back on the formula but he again was just screaming all the time and not resting so I increased the formula. He has gained loads of weight now on a 90% formula diet so don't knock the formula, it does a great job!
I now have a hospital grade pump, I have breast compresses, I take fenugreek, brewers yeast and raspberry leaf extract, and I pump at least 7x a day including at least once or twice between 1am and 5am. I pump for 15m a session and include one power pumping session a day. For a while I was on the pump 6 hours a day power pumping at every session but this was unsustainable. I regret to tell you my supply has never really increased. I get variable amounts between 10ml and 50ml depending on the time of day (so I guess averaging 1oz like you), which comes to about 10% of my babies food a day, or one full bottle.
I reached the stage where I was so emotionally drained from constantly "failing" to up my supply and failing to latch my baby (forgot to mention, baby has recessed chin, slight tongue-tie, and is majorly used to the ease of the bottle. When he is on the nipple shields he just sucks the tip - same as what he does with my nipple but at least it doesn't hurt! ), that I decided to call it quits and just exclusively pump for less hours a day in order to just give him a little milk.
My friend who is a GP told me that the colostrum that you give the baby at first has huge immune benefits, and the first few weeks make a real difference, but after that it's negligible. I know how it feels to desperately want to breast feed - especially after a difficult birth. I started to feel like I couldn't bond with my baby without breastfeeding - which is crazy. If you feel like this, get your baby sleeping on your chest and get as much skin to skin as you can - especially if you were robbed of this at first. Not to fix your supply issues but just to cuddle and bond and relax with your baby. I can't recommend it enough - those first weeks I was so distraught and desperate around feeding I was missing that cuddle time as I was always thinking "I need to pump or my supply will drop" and in my experience you just can't pump and cuddle at same time - I couldn't anyway.
I'm now pumping 2.5 hours a day instead of 6 - cuddling my baby skin to skin as much as i can, and have basically given up on breastfeeding. i will continue to try latch him as and when it is relaxed for us both, which is practically never! I haven't closed the door on breastfeeding but I've basically told myself its not going to happen and my aim now is just to continue giving him little bits, around 10% or so breastmilk, but by bottle. Giving in to the formula and admitting that the obstacles against breastfeeding may be too high in my case is a huge relief mentally. I am no longer aiming at (what feels like) the impossible and so I don't feel like I'm failing every day.
I am going to speak to my dr about Domperidone - at first I was concerned in case it would have an effect on baby but my health visitor today told me it used to be prescribed to premmie babies in the NICU for reflux issues, and also the amount they get through your milk is negligible. Its my last shot at increasing my supply - it may work, it may not... worth looking into if you still really want to up your supply and have tried everything else. Other things that were recommended to me (which I've been doing for 2 weeks now with no results): breast compressions, warm compresses, double pumping, power pumping, pumping 8-10 times a day (ok I never managed that one, occasionally I get to 8x a day but usually 7 when my baby feeds), fenugreek, brewers yeast, blessed thistle (can't find this one so not taking), raspberry leaf tea, loads of skin to skin with baby (like i said i never managed this whilst doing my insane pumping regime) and a hospital grade pump. But essentially none of these are the magic bullet and for some women, like me, they don't work.
Good luck, and remember as others have said - your mental health is really important too. I found my obsession with trying to breastfeed was making me so miserable I was veering into depression and wasn't bonding with my baby, which is crazy when you think about it. A fed baby is a happy baby, and your baby will love you and attach to you no matter how you feed them. Ease up on yourself, you've done amazingly and its clear how much you care for your baby and want to do the best for them - trying your best is the best you can do xxx