Oh Sara are you still having problems :-(
Neocate LCP and Nutramigen AA are 100% amino-acid based formulas. Very hard to explain but it contains no whole proteins. It is for babies with severe allergies. It's available on the NHS but very expensive for NHS (around £30 for a tin that will last 3 days) and it usually only prescribed by a paediatric dietitian or consultant paediatrician although I understand that this varies from area to area. Most will make you trial the other milks first - usually Aptamil Pepti or Nutramigen LIPIL. Nutramigen LIPIL is the most vile tasting of them all.
I have 6 sealed tins of Neocate I'm happy to post if you want them?
We trialled Alex on Neocate for 6 weeks and I did see an improvement in his reflux but TBH he absolutely hated the taste of it and screamed at every bottle and because he already has feeding and swallowing issues it just wasn't worth it for us. We found that flavouring it with golden syrup or brown sugar helped.
I know you are already on an elimination diet, can you remind me what you have excluded from your diet? Elimination diets are SO difficult and frustrating. Usually the first foods recommended for elimination are dairy, eggs, nuts, wheat and corn. This means that the diet can be quite restricted but to rice, potatoes, organic meat and veg.
EDIT - Sorry, I thought you were in the UK so I'm not sure about the difference between milks here and NZ x