OP - if you actually proceed with your plans, maybe consider a wider end at the "head spot" so you can also practice cut shots?
I'm not a table tech, but i have worked with all the materials. During the late 70's/80's i made tools and supplies for a table builder. Since you are not actually proposing a table, i don't feel out of place commenting. :wink: Per some of your Q's on the other post, slate saws easily with a diamond blade in a skilsaw, cut it outside layed flat on shimmed sleepers, with plenty of water going. Use an accurately place batten for a saw guide, you will never see the line once the cut commences.
Granite is more difficult. Gabro is about the best material, in between in "difficulty".
Slate is a little tougher than granite, reason granite is usually spec'd thicker for same app. Though in a section as your propose, either one requires delicacy, and adequate support at all times to avoid creating multiple pieces. I would not spend extra for either material in long lengths given the risk, assemble 2 or 3 lengths as per a regular pool table.
Slate liners are traditionally *poplar, but can be anything. Ideally the wood is reasonably stable, takes staples well, not so soft they don't stick, and not so hard they won't go in or are impossible to remove. "Good" mahogany with straight grain would be a good choice, too.

Whatever you use, on a "table" that long x narrow, don't count on the wood not moving over the seasons. But if you use 3 pcs of "stone" and have some sort of leveling options, it could work well.
*If i was using a wood material for support and not as a staple matrix, I'd probably use something like clear straight grain vertical grade Douglas fir or Sitka spruce. But that would be costly, and you won't reliably find either at a big box, dry enough to use. Rarely the Doug fir, if you know what to look for and have time to dry it and the equipment to work it; including rip and laminate for stability. Poplar works, is not quite as stable, and is more difficult to sort for true straight grain in long lengths.
I don't know how stable glue lams/micro-lams or/ LSL "timber strand" beams are, but they would be worth exploring and are cheap for the size and volume of material. Imagine used correctly one of those products could be good support, poor staple material. Just make sure whatever lumber product is dry at point of machining, & at set up.
smt