The tap drill for a 12-20 is #19 (.166") for 77% thread form. If you used a 3/16 (.1875") drill, that would result in only 44% thread form.
If you broke a HSS tap using such an oversized tap drill, something is WAY out of wack.
That Hillman stock is the poorest quality I've ever experienced and there certainly may be hard spots/impurities, but with a 44% tap drill ???
Another factor is that you may have bought hot rolled material which has the mill scale present on the surfaces. That scale can be very hard and abrasive. It's a good idea to, after tap drilling, chamfer (countersink) both sides of the hole to larger than the major diameter of the thread (.216") so the tap will never touch the scale.
As far as the availability of replacement taps, I would Google "special taps" and contact some of the many USA options. If they won't sell direct, ask for contact info for some of their major distributors.
Good luck.