Sam,
When it's turned upside down, you'll have probably two corners that touch the table/bench and two that don't. You'll want to put the dowel under the two corners that touch the table/bench and clamp the two that don't. This will "over compensate" for the warp; bend it against the warp and at a distance greater than the warp's lift. Once it dries and it's released from the clamps, theoretically it will lay flat once turned right side up. It usually takes a couple of "tries" to get it (close to) right.
Oh, this method will work for large resin parts too....except heat is used in lieu of water.
Felt feet, as mentioned by Scott should, IMO, always be used on a base...99% for looks. In the case of a warped base, they'll aid in keeping the base from rocking, but as long as the wood's warped you'll not have a "straight edge" and that will always be seen.
I would consider giving my method a try. If it works, great. If not...sorry. I'd then spray the bottom with a couple of light coats of your clear. Light coats (stains, primers, sealers, gloss, matt...all the same) are always better than heavy coats....just like paint on a model.
Hope that clarifys....
Mike
p.s. I really like your roadway/sidewalk....very nice.