Bubandbumpjust a thought, but is there any chance your DD could have a tongue tie? It's just now you mention the bad latch.... there is a school of thought that associates reflux with tongue tie and other oral irregularities.
Have you seen an LC at all as of yet?
Fraid I don't know of any LCs with a specialist interest in reflux , wish I could be of more help.
When I had DD I saw a very helpful lady called Katherine Fisher, see here. I think she's based in Croydon but she did travel to me in Kingston, and she seems to have an interest in tongue tie so it would mean you could get that possibility checked out.
Eeek, don't call the number given on that website - it's really expensive! Her contact details (and normal landline number) are listed under 'tongue tie dividers' on the Lactation Consultants GB website here (scroll down to 'London'.