See Mark's blog today. There people tried no fiber for 2 weeks. No fiber can be achieved by drinking bone broth and/or beef broth and eating only meat and fish. It certainly reduced inflation. After that they added in varying amounts of fiber, on an individual choice bases. Soluble fiber is much preferable to insoluble fiber. So veggies are better than grain. Nutrition charts can tell you how much fiber a vegetable has. Juicing will reduce the length of the fiber and the length of time it takes to digest, but it can't reduce the amount of fiber or affect the type of stool that results. Fruit is often high in fiber but you'd have to check each one out. It's also high in sugar which is not helpful. You also want to remove as much sugar as possible. I'm talking, as the sudy did, of a short period of time. Over a long period of time you really need a balanced (primal) diet to be healthy.
As for the amount of time to expect, that depends upon the amount of inflation and your age. Young with high inflation, maybe 3 months or more, again depending on how dedicated you are to the diet.
For joint pain, eat no nightshades ever and add tumeric to everything you can.
I've never tried protein shakes so I can't really answer that question. I've always though real food was the best but then I have time to arrange that.
You might want to get a C-Reactive Protien test to see just how bad your inflation really is.