I had 91st/98th centile chunk of a DD too. She was DC4 though, so, put frankly, I was far less precious about breastfeeding than I had been with my firstborn.
I started mix feeding by 4 months and then was fully formula feeding by 5-6 months. This meant that i could massively increase her daytime feeds. Dont worry you can do this breastfeeding to, so if you want to carry on EBF, you can.
I was giving full feeds every 2 hours through the daytime. By "daytime" I mean 7am to 11pm, i.e. my daytime - 7am 9am 11am 1pm 3pm 5pm 7pm (bedtime) 9pm 11pm. Not snack amounts, but the amount other babies her age were having every 3 or 4 hours my chunk was having 9 times per day between me getting up and me going to bed. I'm talking over double the amount other babies might have.
So my first suggestion here is calories. Feed, Feed, Feed, Feed, feed.
Next - dummy. Some babies don't take to them straight away but it's worth the perseverance. Without question dummy use will be less painful than controlled crying and/or sleep deprivation.
Next - bouncy chair for naps. With dummy and with baby jam packed full of calories through our the day. Then be relentless about it. Sit on the sofa, bouncer at your feet and just keep going and going and going with your foot- relentless and non stop foot bouncing.
Next - limit awake time through the daytime. When baby wakes up, look at the click. Feed baby, have a play or cuddle and then once the clock says 60 minutes from waking up - back in the bouncer. You want baby back to sleep within 90m max. Repeat this all through the daytime.
Finally - talk to the doctors about post natal depression. No-one gains from being a martyr. Get the medical help you need for your mental well being.