When I install a patchbox, the first thing I do is to place the box on the stock in the position that I think looks best, then I put a witness mark on the stock and generally outline the box with a light pencil mark. Then I remove the lid from the finial and then make the finial dead soft and inlet the finial. You will find that if the brass is dead soft you can easily bend the curve into the finial by finger pressure or by using an adjustable wrench and gently bend from the center of the finial out. I will use screws placed in the appropriate position to hold down the finial to make sure the finial doesn't wander all over the stock. I inlet the hinge area first, then work my way up. Once the finial is inlet, I attach the lid and proceed to inlet that as well. I leave the buttplat on untill the lid inlet is just a small distance from the buttplate, then I drop the plate and finish off the inlet of the lid. Once I am satisfied that the lid is where I want it, I use a sharp pointed scribe to scratch the under side of the lid, that determines where I need to trim it off at. When I cut the the lid I do not cut on the line, but just leave the line, this allows for slight hand filling to make the fit as best as I can. In some situations I leave the lid flush with the plate and in others I inlett the lid into the butplate and that I determine well in advance.
Oddly enough, the extra brass on the lid and side plates makes a great way the hold the lid when you are cutting for a final fit, just clamp it in a vise if using a hacksaw.
When inletting the finial, I use a very small piece of wood, rectangular in shape, to tap on the finial with a small ball pean hammer, I gently tap on this little block of wood so as not to dent the dead soft brass.