G'day,
I've just looked at five catalogues that were handy, none American - Renniks, Macca's, Gadoury, Seaby - and none give thickness.
All specify weight.
All but one gives diameter.
Thickness is just not a standard that we use.
Back to your problem: my initial suspicion is that these items described as "unbelievably thick" are fakes, that utilize thick planchets to get the weight correct.
If you look at Spanish Dollars, French Ecu, or British Crowns, they are all about 37mm and 28 grams, or so.
But the forgeries are typically 20g, or less, even though diameter and outward appearance are OK.
Even lead, or tin, which don't "look" right, are significantly less dense than silver. So forgers are left with either an underweight "coin", or perhaps an overly thick one.
Peter in Oz