I have witten about the composition of these stones in my book The Amazing Liver Cleanse (1stbooks.com). If you don't have a gallbladder, you can only pass non-calcified stones. many of the stones that are released from the bile ducts of the liver (known as intrahepatic stones) consist of organic matter, most often bile constituents. They can also be clumps of fat, with trapped food proteins. When these come out, doctors just think they are organic stuff, namely fecal matter. Most doctors haven't studied the subject of intrahepatic stones while in medical school, just as they don't learn how to identify the causes of illness. We cannot expect them to enlighten us about the stone formation. There is virtually no reference for intrahepatic stones in the chemical labs, the only category left for this kind of substance is "fecal matter," especially since many of these stones are loaded with the same bacteria that occur in feces. Medicine only recognises calcified Gallstones as "gallstones." For everything else there is no name, no category, no reason for them to exist. So if you send them samples, don't expect an intelligent response.
You mentioned that you felt your gallbladder when you passed your stones. This isn't an illusion, I have had the same experience with numerous patients of mine. Just as 90% of people with limb amputations still feel pain there, removing the physical gallbladder doesn't mean remove the etheric gallbladder. The merediens that passed through the limbs or gallbladder before surgery are still there after surgery but their Chi-flow is interrupted as a result of the invasive procedure or a pre-existing blockage. This can cause pain. I have developed a system called Ener-chi Art (http://ener-chi.com) that restores Chi flow through any organs or system within seconds, thereby optimising the energy distribution through the etheric organs and systems, even after surgery. In the case of a missing gallbladder, this has helped many people to improve digestive functions.