My growing conditions are the same as Greg's, lots of winter and spring rain, so leaf litter/leaf mold/leaf compost would hold to much water and rot the semps.
I do find that the forest type compost works well mixed with the chicken grits (crushed granite), pea gravel and/or very coarse sand. Play around with a mix that works for your growing conditions.
I like the idea of planting the same variety in different conditions to see what works best for you. Just don't use any soil that is heavy and will compact, sure death for your semps.
I don't fertilize, and seldom water established semps during our summer drought. But the young plants have to be some what babied along that first year.
Marilyn the one shown in your link for S. 'Cobweb' wouldn't be the same arachnoideum as 'Red Cobweb', as the one you show is much smaller than 'Red Cobweb'.
Many nurseries will give a name to plants that are just a descriptive name. I find no reference to there being an actual hybrid with the name S. 'Cobweb'.
That being said, that is an adorable semp.
Cruddy how long have you had semps? Sounds like yours might need some protection for afternoon sun during the summer, or shade cloth over a frame?