And that's the Royal Model conversion set. It looks like it might be a pretty good starting point.
You'd still need to backdate the radiator "hump" in the rear as well as the turret roof to make an early M13/40.
Brach Models offers a couple of full-resin M13/40 kits (different production series), but unfortunately does not sell a conversion kit. The Brach kits have generally good reviews.
Of the two styrene kits, Tamiya and Italeri, the Italieri M14/41 is the only one that's accurate.
The Tamiya kit has features of both the M13/40 and M14/41 not to mention fundamental dimension errors because of its "motorized toy" antecedents (this includes Tamiya's updated re-release). In the end, the Tamiya kit is neither an M13/40 nor is it an M14/41.
Fortunately, the Italeri kit is actually a quite accurate M14/41 even if it's a little soft and basic in the details.
You can kit-bash the Tamiya and Italeri kits together into an accurate M13/40 if you're willing to do the work. It's not particularly hard. The Tamiya kit is not absolutely necessary for this, but it does have a few useful bits.
Here's a build blog with my M13/40http://www.armorama.com/modules.php?op=modload&name=SquawkBox&file=index&req=viewtopic&topic_id=198082&page=1
Here's the research / reference info that I used for the build: