Never heard of that issue. Perhaps a short with a thinner chamois might help. Even one with an old school real chamois with no foam or other fabric would help. Thinking the edge of the chamois is the issue as you mention. Make sure the shorts are form fitting, as that is a key function of a riding short for it serves as a second skin. If wearing baggies and you have not tried traditional cycling shorts, give them a try since there is no extra fabric to cause problems. In addition, if all you have used are mid grade shorts give a high end short a shot. Be sure to start with a name brand, not a "private label" brand since there typically are differences in quality of chamois, fabric, and fit.
Ps. An old friend of mine in the garment industry explained why name brands cost more by using this comparison: They do the research, development, marketing and understand what they do and why they do it. The off brand stuff are copies of the name brand stuff but are constructed without an understanding why they are doing what they do. Apply this to bridge construction and ask yourself who you would trust. My addition to this explanation is looking at the bike industry as an example. Shimano makes good stuff, there is a brand out there that looks just like it, functions like it and cost a fraction of the Shimano stuff. It is called Falcon and other names that they put on it. But somehow the stuff literally lasts less than half the time Shimano lasts. How come?