It can be confusing for a patient seeking rhinoplasty. So many methods and opinions exist which may vary surgeon to surgeon (as you discovered). Sounds like your goals are: to narrow the bones, lower the hump on the bridge, refine the tip, and narrow the nostrils. These are common goals but the appropriate techniques to use would depend on certain features of your anatomy. Without seeing pictures and having the luxury of a physical examination, it is tough to provide details about a plan.
However, one useful bit of information I can provide has to do with skin thickness. Generally, rhinoplasty is an operation in which we change the form of the bone and cartilage of the nose. Once this is done, the skin then has to drape cleanly onto this altered infrastructure in order for there to be an overall positive change in appearance afterward. Before surgery, each nose has the exact right amount of skin for the infrastructure beneath, like a glove fitting a hand.
After surgery in which there is reduction, narrowing, or lowering of this infrastructure, there is too much skin. If you have thin skin, the skin envelope can contract and shrink somewhat so that clean draping will occur. If you have thick skin, however, the skin cannot shrink that much and you may end up with a permanent relative excess of skin. This may lead to thickening of the skin and an appearance of skin fullness or bulging, sometimes called a polybeak deformity. If you have thick skin and want to look narrower or more refined, it may require building up some areas of the nose so that the infrastructure pushes into the thick skin envelope to create a more narrow and refined appearance.
This issue with the skin thickness is just one of many considerations with regard to which techniques are best for any given rhinoplasty. Though forums like this are helpful to provide information, they cannot replace a thorough evaluation with an experienced rhinoplasty surgeon so that all of these issues can be explored.