Good news: If you know where to get them, You can get short scale strings in any type of string and gauge, just like the long scales.
www.juststings.com has the widest assortment of short scale strings that I have found.
If you want a deeper, less bright and thumpy sound, you should go with flats. Thomastik-Infield has a short scale set in medium gauge that would probably meet your needs. They are not cheap.
GHS has a short scale set for every type string they sell, and some are in medium gauge although most sets in this scale are lights.
D'Addario makes an XL set in medium gauge that are .45-.105, but they are rounds and a little brighter than probably what you want. They make a set in their half-rounds and chromes as well, but I think they are light gauges.
Another good alternative would be the set of tapewounds. Both LaBella and Rotosound make a set of short scale tapewounds in .50-.115 gauge, and they are noted for their deep thumpy sounds.
GHS Pressurewounds split the difference between flats and rounds. The sound of a flats with the lower tension of a round. I am not quite sure if they come in medium gauge.
Best of luck with your search, and I hope you find the perfect strings for your needs.