You haven't answered about the thickening milk but we had this problem with formula called Bebilon Comfort which was for colicky babies. It wasn't for a refluxer but still they have thickened it and when we were using Avent bottles with teat 1/2 or even 3, nothing helped as just the small holes in teats were blocked. DS immediately was refusing a feed so I knew something is wrong but he was a baby who only feeds for food from breast and bottle, never for comfort. If she feeds for comfort, I guess she might be not bothered by stucked holes but it will still prevent her from taking more from the bottle.
What worked here was using a 3-flow teat from Avent. The case was that it has a cut instead of a hole so it couldn't be blocked by thick milk. I used the slowest flow on it but DS could easily drink from it. Using normal teats with 1/2/3/4 holes didn't matter, as no matter how many holes there were, the milk wasn't flowing:).