Hugs hugs hugs Jen, I know you are struggling right now
Honestly I think put IS to one side right now. Put her in the carrier for sleeps - get her some rest as best you can and give yourself a break from the crying. Sleep training so young is tough, takes time, patience and persistence and the learning curve is slow. Add to that reflux and honestly, IS and the perfect EASY is not going to happen right now. I really would ease up on expectations (I know this is very hard though) and embrace the AP. There is nothing you do now that can't be undone later down the line, often with much quicker results, when you are in a better place yourself and DD is not in pain.
Lots of hugs lovely xx