Interesting project. I am extremely familiar with these components as I work in the dental CAD-CAM industry myself. I think you might need to be clearer on how the part is being held, and from which end. Also the fact that the collar area you wish to machine is not necessarily rotationally symmetric, or else the lathe would be the obvious choice.
I guess it is a little strange why you would use a Sherline to do this sort of component. The enormous value of abutments means that surely you could afford to push out the budget a little further? Regarding your software question, this could be done with any of the big boys' systems (e.g. Delcam Powermill) but not for the budget you've mentioned. I'm sure someone will will suggest something that will work though.