I know of the Leica Monochrome (black and white) camera, but it is too expensive for me (my budget is about $1,200). Is it there a service that will modify the sensor of a camera to make it truly a B&W camera? Has anyone had experience with that conversion?
A monochrome conversion is not feasible (it would require removing of the Bayer filter and a major rewrite of firmware).
But it is not really necessary, as the monochrome conversion can be easily applied in post processing, and any increase of sharpness is - in context of modern sensors, which are not resolution constrained - Leica marketing hot air.
More to the point: a major aspect of monochrome photography work is tweaking intensity of different colors / wavelengths. In the olden days of film this was done with color filters (yellow, orange, red and what not... ).
In digital workflow it is done not in camera but in post process, but you require a color raw file to start with. Your flexibility increases, as you are not limited by the range of filters available, and you can make multiple final images out of original raw file just by changing settings - it is actually quite educating to learn about filter effect.
maxmax.com can replace some Fujifilm digital cameras' sensor with monochrome one.
There are rumors that Fujifilm considered monochrome X100*, but got enough positive feedback from opinion polls.
(consider also switching to film camera with B&W film, as I did :) ).