You have the more common straight window cabriolet I believe they made like 25,000 of them off the top of my head. Cabriolets are one of the exceptions. They frequently get over $25,000 on the market when done (used to be over $30k but I am not sure today). You can restore a cabriolet nicely and not get more into the car then it is worth.
Only about 6000 slant window cabriolets were produced. There are about 400 known to exist today.
To answer your questions.
Depending on what you have you could have something that a restorer would want. Does it have any of the cabriolet specific top parts or most of the original wood? Lack of cabriolet specific parts affect its value as they are challenging to find.
It is not rare enough that it would be a great loss if it was rodded. The usual problem with rodding is they are a wood built up body. They take a lot of work to do them in metal and they do not turn out very good. Out of the 10 or so I have seen only 2 looked good. One was a high end pro job and the other was a slant body bolted on the typical rod chassis. In both cases the bodies were left intact, not chopped or channeled. The others were done like a roadster which just does not work.
The cabriolet was a top of the line body. Somewhat stately. You bought one to say you could afford a nice car. A roadster was the bottom of the line car. I think it needs to be rodded with that idea.
My opinion,
You want to keep the high end unique features. You want a top that works and door windows that work. You now have a year round car that you can not get with the roadster. Clean up the lines, lose the landaus and away you go. Look at the 32 cabriolet lines for an idea. You will also want to taper the rear top forward some. They were originally straight up and this will require that you taper the belt wood so you do not get a line.
The big problem you get from the aesthetic side is the windshield posts.
They stick straight up. So if you drop the front they they tilt too far forward and kill the fast look. Keep the body more level and set up the chassis less like a straight line power car with the front dropped and more like a high HP driving machine. Go for handling and comfort and you capture the high end cabriolet in a rod. I think the car done right will command a premium. You will need to put the body on a very solid frame. The cabriolet body is very flexible which is why they had landau bars.
If you rod it, please send me some after picts so I can see what it looks like.
Anyway, my 2 cents.