Ceramic Waffers

A thickness of 0.004" (Not 0.048" or .004', right?) is possible through chemical-mechanical planarization, commonly called lapping. Excess material is gradually removed from the planar surfaces until the desired thickness is reached. My company has successfully used this approach to make piezo-ceramic elements 0.003" thick, which then had to be cut to size by laser.

Alternately, you could try using an abrasive-waterjet cutter or liquid-cooled abrasive cutting wheel saw to dice these wafers off of a block of your material. Some cutters can achieve a tolerance of +/- 0.001", so it's almost as reliable for thickness dimensioning as most lappers. However, there may be some surface effects and breakage at the edges of these wafers; and a higher risk of the wafer shattering during cutting. I've never tried this approach (or heard of it being done) but it should be possible.

Your biggest problem will be the size of your wafer; 4" by 6" is a huge surface area to keep a tolerance across and will definitely increase the chances that handling or assembly stresses would cause fracture. Keep in mind though that some ceramics have better elastic moduli than others and will tolerate higher stresses. Your success in attempting this will be most affected by the material you choose. Likewise, your housing material should be rigid enough to limit the stress transferred to the wafer layers. Any intra-layer adhesive should be a compromise of flexibility and rigidity as needed to dampen internal forces. Good luck.