Turntable Mats: Rubber, Felt or Cork.

What material(s) have the same, or very similar, hardness as a typical vinyl LP?

To my mind the obvious place to start would be similar to Noromance and myself have already done.
An album, be it a vinyl 10" or a shellac 78 as a mat.
Well worth a trial IMHO.

Many years ago when I was trying different mats on an old Rotel RP 850 I concluded that the best mat was another LP!  Are there vinyl mats out there?

There are acrylic mats for sure, not sure if any thing made that is same composition as a modern vinyl record though.
Bar another vinyl record of course.

Delrin if you’re obsessed with matching to vinyl.  TTW used to make them. Colby Lamb can make them. And if you read other posts, what could match the hardness of a vinyl LP better than another LP? At least two others have mentioned that.

VPI’s used to make platters with a top layer of Delrin. The Aries 1, TNT-3, and TNT-4 had 3/8" of Delrin over 7/8" lead-lined aluminum, the TNT-5 7/8" Delrin over 5/8" stainless steel.