Contact someone who belongs to an antique farm power equipment association. A stream engine association is a possible place to start. Those folks are always looking for stuff to show, the weirder the better, and you do have an nice 'contraption'. From what is could see, the mower has all its parts. This is a big plus.

One problem you might have is getting a fair price estimate. Many of those collectors operate on a shoe-string and pay as little as possible for a fixer-upper to fiddle with. They do a lot of friendly trading among themselves.

The other place to look is ebay, but the prices found on ebay are often low. Its what the item sold for (from bids).
You could get an appraisal from someone who works for an auctioneer business. If the price is too low for your sensibility, keep the item for awhile longer. Once the word is out that you have such a thing, someone may make an offer.

Remember that price is a function of age, condition, desireability, and rarity.

Personlayy, I think that would be a fun project to restore.

A golfer with his own bent grass putting green would love to have one of those.
Casey

This unit ran and cut the grass when I stored it 15 years ago.I contacted Jacobsen and they said it was one of 1250 made and the reel unit was one of the attachment that could be bought.There were two other attachments offered.The reel unit was one of 599 made.The unit is # 647.