Let's see if I can address everything you posted ...
First of all, here are the "official" stacking sandwich recipes from the Spellbinders website:
Big ShotTM (Black & Pink) by Ellison-Sizzix® and Big ShotTM for Stampin Up by Sizzix®
This machine is capable of cutting and embossing any Spellbinders Die. You will need Spellbinders two Tan Embossing Mats to cut and emboss in the Big ShotTM machine. Cutting Sandwich - (Stack from bottom up)
1. Place large platform down first with all tabs closed.
2. Place Spellbinders die face up, (that would mean ridges or bumpy side up).
3. Place card stock on Spellbinders die.
4. Place two Big ShotTM acrylic mats on top of cardstock.
5. Roll thru Big ShotTM machine to die cut shape.
Embossing Spellbinders Dies in the Big ShotTM by Ellison-Sizzix® and Big ShotTM for Stampin Up by Sizzix® Embossing Sandwich-(Stack from bottom up)
1. After cutting, remove acrylic mats from cardstock and die.
Leave the Spellbinders die in place with paper die cut out still in the die on the multi-purpose platform.
2. Place TWO Spellbinders Tan Embossing Mats on top of die.
3. With one piece of 12x6 card stock tri-fold for a shim and place on top of the Tan Embossing Mats.
4. Place ONE Big Shot acrylic plate on top and run thru the Big Shot machine.
These sandwiches are the ones they (Spellbinders) came up with for "optimum" results. However, I am sure you can achieve similar results using the black embossing mat. Anyone have a sandwich that has worked for them using it? If so, please let us know! I may fiddle with it a bit and see what I can come up with ...
Okay, so now you say you have issues with the black embossing mat CUTTING into your cardstock? Hmmm....I am not sure I understand. Is it actually cutting a line or just embossing one? I may need a bit of clarification on that one.
Next, in order to achieve the 1/8" mat, you will need to have BOTH the large and small sets of circles (or whatever shaped you are cutting). Each set, by itself, nests in 1/4" increments. If you have BOTH sets in any particular shape you can use them together (for example take the large circle from each set) to achieve the 1/8" mat.
Lastly, in order to keep the die from "slipping" ... use a piece of "removable" tape (i.e. stick a piece of scotch tape to the back of your hand and then peel it off ... it has now got the "removable" feature going on!). Tape the die in place (to the cardstock) before rolling it through the Big Shot. Then it will just peel off after you have cut and/or embossed your cardstock.
Hope this helps. I know it is a LOT of info, but ya asked a LOT of questions!!