I'd do bluestone.
Clean and degrease the existing slab. Since it's going over a slab you can use cut thin bluestone, one inch thick.
Apply a concrete bonding agent to the part of the slab you're working on, lay a bed of motar, and set the bluestone in the mortar.
There are myriad types of stone veneers, or even outdoor tiles, that can beat the 1.5" restriction. Some will be close, but they'll still beat it.
Find a style that suits your taste and run with it. Bluestone is one of my favorites, 1" runs about $3.25 a sq foot.
Don't forget the bonding agent, though...
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