There are a few herbs that help improve bile. Dandelion, St Mary's Thistle and so on, all help the make up of bile. Usually health food shops can point you in the right direction or a naturopath.
Other items useful is to prepare raw vegetable juices include beetroot as it is good for the liver and bile. Only Apple should be mixed with vegetable and no other fruits. For a fruit juice its best to only mix carrot in perhaps some celery. Try to get these as organic remember you are trying to improve the liver and the bile and toxins from pesticides etc affect the liver.
Yes in your case give the flushes a go, be positive about it there is nothing dramatic about the flush protocol. It should help a lot with clearing out some of the sludge and you will probably notice a feeling of well being. Don't necessarily stop at one flush remember it you took your time in getting the sludge there in the first place so work at removing it too and improving the bile.
If you still have a acid reflux bothering you try two other things. Slippery elm is excellent at relieving acid reflux and Aloe vera to help soothe and improve digestion. The aloe also helps with the intestines.