I can not attest to the cuttability of each sheet but I just went down (they are 2 miles from my work but they do ship also) and got a sheet of 1/4 MDF and 1/4 Baltic Birch Plywood. They cut the sheets down for me to exactly 12 x 20 and I ended up with 15 boards each for about $55.
https://www.woodworkerssource.com/shop/product/14balpack3.html
The other day I noticed Draftboard-like stuff at Johnson Plastics. It’s made by LaserBits, and it is $5 for a 12" x 24" x 1/8" sheet.
https://www.johnsonplastics.com/laserbits-12-x-24-x-1-8-econo-laserable-wood-sheet
1/4" is also available, as are versions with faux wood veneers… and some stuff that looks a lot like Proofgrade plywood, for a few bucks less.
(I was also pleasantly surprised at the shipping cost from JP… I ordered a pile of stuff from them, like 15 12x24 sheets, and shipping was just $17. At a buck a sheet premium for shipping, I am pretty happy. )
Not much in thin whole woods 
not bad for BB if you are in AZ.
yea they have a ton of plywoods but no 1/8 or 1/4 hardwoods - the guy was like - just buy a band saw and cut it yourself - umm ok lol