Doubt you will win.

Full bedded stone had a few centuries of history to prove itself, often required in high end communities, along with "returned" corners to assure its use looks authentic and structural.

Thin cut stone can look like wall paper if not installed with some care and depth around windows and openings., especially if not returned around corners. We're seeing some pretty shoddy one dimensional masonry applications on million dollar homes.

Communities with design guidelines requiring authentic stone may also require real lumber board on batten siding instead of cement board or T111, etc. Keep some budget in reserve for more requirements from the design review committee.

This isn't the only exterior finish choice. It's an option if you want stone. I'm assuming.

Have you asked of the community, "Why do you now require full bed on all exterior walls?"

You may have some misconceptions about stone and should not concern yourself with poor installers bodies.

"... full bed when wet takes longer to dry and is therefore more prone to cracking under extreme weather"

Full bed stone (aka, stone veneer cavity wall) has a cavity behind the stone that allows effective water drainage and drying (not that stone retains much water).

Unless a drainage plane is installed behind adhered thin stone, water can become trapped and freeze in extreme weather and surfactants in the materials that touch the weather barrier can cause it to lose its water resistance.

Whatever system you use, find a mason who knows how to build it properly and find someone to oversee the work.