The Dingwall will never sound EXACTLY like any Leo Fender creation, but you have a better chance of getting in that ballpark with an all-maple neck (which Leo used often).
Julian, we're gonna have to "agree to disagree" on the effect that wood has on tone.
I'm not saying that wood outweighs strings or pickups in the overall tone, but all else being equal, many people can clearly hear a difference in a bass with a maple fretboard from the same bass with a rosewood fretboard.
Same thing with body woods -- the cellular structures and oil content are different, which affects how the waves propagate through the medium.
That's basic physics.
It may not be an observable difference to everyone once the whole band has kicked in, but it's an ingredient in the "soup".
I dont disagree that those things can make a difference in acoustic instruments. In solid body, fretted, amplified instruments, the level of perturbations contributed to the vibration of the string by the qualities you mention are so minimal, they dont matter.
Now in a acoustic instrument, where you rely on the vibrational qualities of the body to produce your sound it is a different story. The modes of vibration of the top or back of an acoustic guitar will effect the voicing, and thusly the composition of that panel will come in to play to a degree, but I would say that the bracing plays a bigger role. In a fretless instrument the material of the fingerboard will matter, as it will partly determine the dampening on the string. But in a fretted instrument the string makes no contact with the board. The interaction between the fret, the board, the body, and back again to the string are going to be minimal. The way you fret the string is going to matter much more.
The feel of the neck and fingerboard may change how you play, which will change how you sound. But I do not buy that there is noticeable tonal differences.