If you suspect reflux I suggest you go back to your doc and ask for a meds trial or a referral to a paediatrician (not sure where you are, just saying how it works here in the UK where I am). The thing is, if you suspect it and your LO is so disturbed during sleep then really it needs to be followed up again.
Looking at your EASY times it seems you might be keeping her up a little too long, she might be OT (over tired) for her naps which can lead to more jolting (which wakes her) and inability to fully relax for the sleep. I would aim to have her asleep by 1hr to 1hr 15 mins max (I see in you have some A times of 1hr 30 which is more suitable for a LO of 3 months going on 4 months), this doesn't leave a lot of time to feed and get her nappy changed and very little play time but it is worth trying to see how it goes for a few days on the shorter A time.
You didn't mention in the EASY if each of these naps were in the cot or in arms but from your information it looks like she doesn't sleep well even in arms but that you have been trying to start some gentle sleep training. I would put sleep training to one side for a short time, lets just see if she can sleep some regardless of help/props - over the next few days see if the shorter A time plus holding her or carrying her in a sling (with movement, walking, rocking patting, if needed) or in a push chair going for a walk can help her to sleep better. I know ultimately this is not your goal, of course, the goal is for independent sleep and we can help with that but just for now lets see if she can sleep with full help for a few days and if her nap times improve.
It can also really help refluxers to be more upright when sleeping so a sling would be great, or if you need to put her down see if you can elevate the head end of her cot (cot safe wedges and/or cot blocks which have been safety tested. Temporary solutions to try would be a folded towel or pillow under the mattress to give an incline but I would suggest you stay with her the entire nap to ensure safety), some push chairs have a setting for an incline which is safe for young babies. Using a sling can also help with being more able to prepare yourself some food and get to eat it too.
I understand that right now you feel like you are holding her all the time and my suggestions about sleeping in arms/sling unfortunately are not giving you any additional Y time to get yourself something to eat or to take a break - I know - it is hard if you have a LO that isn't sleeping well which is why I think you need to head back to the docs to ask again about reflux and call in some back up if you have any. Often friends and family are only too happy to help out but don't want to interfere and don't know exactly how they can help. If you have anyone, call them, set a time they are to arrive and be clear about what you need (come round I need to sleep. come round and make me some lunch, come round and hold LO whilst she sleeps so I can eat) and really make sure when they arrive you hand over LO and go and do something for yourself, even just for 30-60 mins, you might feel a little better.
hope this helps some