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Is there a place that does granite counter tops by you? They maybe able to make a face cut for you. Just a thought.
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A llyn medllyn should lap fast, as said a low grit sanding belt will get you to flat quickly, or drywall sanding screen in a dollar store cookie sheet, on flat cement floor.
I use 60 or 80 grit Silicone Oxide loose grit in a cookie sheet to get Noviculites flat in a few minutes, from GotGrit.com. A $15 grit progression will get you to 500 grit then switch to Wet & Dry. Once flat, it goes quickly through the grits. You only need a teaspoon of each grit, so a quarter pound will be plenty to do several stones.
Here is an old thread on lapping on sanding screen. Lapping Vosgienne
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You might try your sidewalk to get the heavy stuff off then sand paper to finish up.
