Hi Matthew,
This publication may be helpful to you. It is from 2012 but much is still relevant. I too agree that it's a bit early to consider another round at three months since there has been a response. Your mom's case is a little complicated due prior issues.
https://ashpublications.org/blood/ar...plastic-anemia
You may want to look at the drug Eltrombopag. It's fairly new and I don't know enough about it to comment on its use/success.
It's also a good idea to get copies of the labs and chart them to look for trends vs just individual abc's. Also include, if you have them, blood work results that preceded the onset of all of this.
I assume they ruled out all nutritional issues and GI problems like ulcers/bleeding from being on Naproxan.
If your family is not comfortable with the treatment recommendation, I would definitely seek another opinion from someone who has experience treating SAA. You may want to consider contacting NIH/ Dr. Neal Yound.
I think you should start a new thread under the aplastic anemia section and ask your questions there. It's more specific to your situation and you may get more responses.