Hi, As I understand, your problem is to calculate the maximum amplitude of each string and then design the curve of fingerboard such that strings remain as close to board as possible but don't touch it during vibration.
I found this problem very interesting; because I am a physicist and working on vibration of solids in longitudinal mode and this is vibration in transverse mode. This project is very much related to my experience and area of interest. I offer my services to solve your problem. Apparently this calculation of string amplitude is a simple job and is not more that few hours work. But practically it would take long time. Because vibration depends upon, many parameters, like string tension, thickness, material and so on. I we would have to determine them first. I explain this by following example. Vibration amplitude depends upon the force by which the string is plucked, and practically it is very hard to determine this force. To overcome such problem during design of any thing people usually have to suppose some values or their ranges. So we may also have to do some suppositions and approximations.
I offer you to please consider my bid, we would have an excellent working relation during this "research and development" project.
Looking forward your positive response.
Nasir Javed