Ok, you don't 'need' the money, however much it might be. But like most of us a little extra cash is never a bad thing and you have places that it might be of benefit.
Enclosed trailer...not inexpensive for a decent one. Are you thinking that you may need to change locations and thus make it easier to move the DeSoto? Or would it just be for storage?
If long term storage is considered (park it and forget it for awhile), then you might look into a shipping container. Air and water tight units are relatively cheap but the tare wt for a high-cube 40' unit is close to 10K so it is not something that you can shuffle around the yard. I haven't measured my '47 but I think it would slide into a container. The biggest factor is whether or not you plan to remain in your current location and the potential cost to move the 'box'.
...but, if you are in a CCR controlled area......
Now, in the long term, you're only 40-something. So what is your plan for the post-65 years? You have a lot of hours in the car that would be a good re-start point when you open the 'time capsule'. You also have the interim to continue to collect parts that may be needed without any time pressure.
If you keep it and store it then be sure to put a file together detailing all that you have done and where you 'think' you are headed with the car. Age has a funny way of screwing with formerly intact long-term memory.