I saw your question a few days ago and decided to offer my perspective.
After a fill, I do not drink 'alot' of cold water because I am typically a bit swollen and it feels like a slow pipe. I prefer to drink alot of green tea, Earl Grey and peppermint tea (which by the way is excellent for our tummies and nausea). The warmth feels good and I believe it helps relax my new fill a bit.
Personally, I was once VERY tight and had the same issue you are going through. It took FOREVER for anything to go down. Even just an ounce. After hoping for 6 days things would settle down, I went and had .2 removed. It was like the floodgates were opened.
If you are having to wait for 1-2 ounces of water to go down, I would suggest getting a fluoro...or at the very least .2-.4 removed.
You do NOT want to pooch your pouch (or keep the irritation going and have a slippage).
Keep us posted. xoxo