I get advice

But sometimes I REALLY get advice.  A former co-worker, John, is a woodworker and does restoration work, and he told me step-by-step what to do.  I'm going to share it with you:
It's not hopeless, but it will be a little bit of work. Here's my opinion (for what it's worth.) DO NOT have it dip stripped! It will ruin it. They dip it in hot water and caustic solution which swells the wood. Then when it drys out it shrinks and warps further and cracks. Plus it will stain the wood black around the nails worse than what it already has. You cant' remove the black stains. It's true you can scrape the FLAT parts but be sure to take a file or something and slightly round off the corners of the scraper blade. Otherwise they will dig in and leave gouges that can't be removed. You can't scrape the lid because it's so warped it would gouge really badly. Take a hammer and nail set to the nails before you start so the scraper doesn't dig into them.

After you are tired of scraping, get some nitrile gloves and a qt. of KUTZIT stripper. Go OUTSIDE and apply it with an old brush. Do one side at a time. Remove it in about 20 minutes with med/coarse steel wool. Dip some 0000 steel wool in ACETONE and remove the remaining gunk. Do this again with acetone and a cotton rag like a town up bath towel. Make sure you do the inside of the lid if it has varnish on it. It probably doesn't judging by the way it warped. Sand the carcase all down till you are happy with the way it looks. Don't do the lid yet.

I would remove the legs and the nails holding them on and just make a rectangular base to lift it off the floor a few inches. You can cut a pleasing design in it pretty easily. It should be smaller than the outside by an inch of 1 1/4" all the way around. After you are done with the carcase you will fasten it from the inside bottom using a countersink bit and wood screws.

The lid has absorbed moisture on the inside, causing it to swell and warp. That's why it's important to varnish both sides of it. So now you can try to flatten it or have it sawed in strips and rejoined flat. If you want to try to flatten it try this on the lid next. It should probably be off already for ease of stripping the carcase. After it is stripped lay it in the blazing sun with the convex side up (inside) and let the sun pull the moisture out of it. The grass should be putting moisture in the other side. Bring it in at night and do this for a few days until the lid has warped the other way a little. This does not always work but it's worth a try. Screw three cleats to the inside to help hold it flat. Make sure they are short enough not to interfere with the lid closing. You can probably live with the crack in the lid and it will be part of it's history of being rescued from a barn. A latch on the lid would be worth considering as it would help hold the lid flat also.  

 It looks like a big job. But, break it down into smaller jobs. (1) lid and leg removal, and tightening up nails.( 2 ) scraping and stripping, (3) lid work. (4) make a base. (5) sand and stain and varnish. (6) Enjoy the fruits of your labor. Yes I do commision work but I have to work it into the other stuff I'm trying to do now. Here's another thought, it probably would be nice to have handles on it to help move it around. They would need to be rustic and match the latch !  

A little bit of work?  Sheesh.  I'm going to see how much it would cost to have a professional do it.  Yes, I know it wouldn't be necessary to "do it right", but John has given me a desire to see this thing done up the way he describes.