Epoxy is kind of expensive for a casting job.
I have done a similar thing using a product called "Durham's Rock Hard Water Putty".
https://www.ebay.com/itm/Donald-Dur...852315?hash=item2145602f9b:g:DfgAAOSwDRxbamRz
Similarly, place the stone flat (top side) down. I built a casting dam around the stone using strips of wood and affixed it to a piece of plywood. Lined it and covered stone with "saran wrap" type plastic.
Mixed the Durhams rather thinner than specified on package so it is pourable.
Poured enough into form so it covered stone plus about 1/2" more.
And vibrated the whole form/stone/casting material with a pad sander with no sand paper in it, which causes the thinned down putty (a shear thinning material at this mixing ratio) to settle and fill the mold pretty near perfectly.
This putty hardens via chemical reaction and does not shrink appreciably from the as cast size as it dries. Net result, a custom base which is NOT glued permanently to the stone. I made a base for the combination of cast base/stone to set in.
This casting material can be cleaned up with water before it hardens but is not much affected by water once it hardens and thoroughly dries. I have not bothered to further lacquer or seal the formed stone base, it hasn't crumbled after ancouple of sharpening sessions.
