protecting confidentiality of a spatial point pattern

Hi everyone. I'm looking for your perspectives and suggestions on this. I have geocoded point locations of a health event (cases) and non-events (controls), in an area of about 5500 km^2. A colleague, who is not authorized to have the true data, is developing a new method of modeling case-control point patterns, that would be very useful in understanding this health problem. I am OK sharing the locations each jittered randomly within 5 km or greater radius. But this degree of jittering makes "tuning" the new method of spatial modeling rather challenging. Colleague would of course prefer a smaller radius of jittering, but I am hesitant, especially for the rural areas where buildings are sparse. 

Any ideas on best way to obscure the true locations while preserving utility for model development?  

I've thought of "salting" the data with randomly generated points that are neither case nor control locations--simply fabricated points, then jittering. To add further uncertainty. Would this help? What minimum fraction of fabricated points would be sufficient-10%, 15%, more?

There is the option of preceeding the jittering with a translation and/or rotation--move all points a distance and direction and angle known only to me.  But I worry that with readily available  substantive knowledge (like my name, institution, and general jurisdiction of activity), one could back-calculate the true location of the regional centroid, which would reveal the distance/direction/angle of transformation that was applied to all the points.

I could change the whole point pattern to another UTM zone, but that leaves the same problem--anyone aware of my UTM zone would know the origin of the data and could shift it back.

Change the shape of the region that contains the point pattern too, then jitter it? 

I'd welcome opinions. Thanks.