R, two notes on preparing any panel that you choose to work with:
First, seal the reverse side too. Warping is caused by an imbalance of moisture, so if one side is coated and can no longer absorb moisture, and the other is bare, it will be able to absorb moisture unevenly and warp. If, as one side is coated, the moisture from the coating causes warping... then coating the reverse side counteracts the warping, and once dry it remains flat, if it does absorb any moisture from the environment, it will do so slowly and evenly.
Second, shellac might be a good option for sealing, it is commonly used to cover stains and knots that bleed through paint. Shellac is natural, has a yellowy-orange hue, and you can buy it as dry flakes that you dissolve in alcohol or pre-mixed in a can (there's a few brand-name 'stain-killer' shellacs that are tinted white). The best part, is that it dries FAST ! like ten minutes, so recoating goes quickly, and each new coat dissolves into the prior ones...
The 12" x 12" size you are using is likely to be considered "scrap" by most woodworkers. If you know any local woodworkers, furniture or cabinet shops, you might inquire about what they could let you have from their scrap bin. You could take an assortment of material types to test out, as is, in whatever size/shape they might be. You could also ask if someone could trim some of the "scrap" into the size of squares you want (or rectangles). If you have gotten in the door, and they didn't already say "But we're not cutting anything!" then they might consider that quick task as well. They could invoice you an actual (nominal) fee if they are real sticklers, or it could cost a small bribe like "beer-money", or cookies or brownies, or it could just be free if they aren't busy.