qgis - How to generate random points with minimum distances between points in multiple polygons

I am looking to create random points for a random stratified survey. There are three different categories being surveyed; for each, I have a single shapefile, each containing a number of polygons.

I would like to generate a number (undetermined) of random points in each shapefile, with a minimum distance of 250m between points (regardless of what category/shapefile they are in). In other words, I would like there to be an equal number of random points in shapefile1, shapefile2, and shapefile3, with no point within 250m of another (i.e., a point in shapefile1 should not be within 250m of another point in shapefile1 or a point in shapefiles2 or 3). If possible, I would like to create the maximum number of random points possible given my minimum distance of 250m limitation.

So far, I have been able to generate random points (using ArcMap and qgis), however the minimum distance between points seems to apply only to points within each polygon, rather than all polygons in three different shapefiles.