You are taking on a big job with uncertain results, but if you want to try to lap the smaller piece on the larger one:
use loose grit silicon carbide - get it from a lapidary supply or on Ebay.
Start with 100 grit and put a small amount on the plate and add a tsp of water and a squirt of dish soap. spread out and start lapping. Apply even pressure, and don't go beyond the edges more than 1 inch.After the surfaces are evenly frosted, clean well and switch to 220 grit. Repeat. Then 400 grit ( or finer). If the plates are for lapping with sandpaper and such, they don't need optical polishing.
Another way that might work for just making then fairly flat is to use a ceramic or diamond flatting stone. They are used to true up water stones and come in 3X10 inch sizes. Use lots of water and work the entire surface with the flatting stone until it is evenly frosted. They are usually 100 grit or so.
Your post brings back memories of grinding and polishing an 8" parabolic mirror for a telescope back in the 80's. It took many weeks.
Stacy