Makes sense.
I like the idea of dissolving them. I use malic acid and I have tried GCG, and Chanca Peidra a couple of bottles each. Maybe I didn't stick with them long enough but I couldn't really tell a difference.
By bitters do you mean fresh greens? (dandelions)
Dandelion greens will work. Bitters are any bitter tasting herb. The bitterness leads to stimulation of the vagus nerve, which cleanses the liver and increases bile secretion. Increased levels of bile help dissolve the gallstones. Other herbs that can be used include gentian root, picrorrhiza, mugwort, etc.
Lecithin and fibers are also very important for bile formation.