Sanders,
I have exactly the same dilemma. I have a II from the first year of production (1932, so of some interest to collectors), that I use regularly. Unfortunately, at some time in the past, it was converted to flash - very badly as it happens, as the flash socket was mounted on the front, just below where the slow-speed dial would be if it were a III. The flash socket leaked light and every frame on a film had a white stripe somewhere across it (depended on how long it stood between frames being exposed, how quickly you wound on, etc).
The only solution was to remove the socket and blank off the hole. So, now I have a nicely brassed II with an ugly (to me) repair that stands out like the b*lls on a bulldog. Apart from that, the vulcanite is really quite good (unlike my Standard, where it is about to fall of in large lumps). On the up-side, the problem with the light leak has meant that the body was probably little used between being converted and it coming to me, so mechanically it is very good.
Given that the camera is intended for use, not just to be put in a glass case and have sugar thrown at it, I'm also considering recovering. I have done two III bodies with the Aki Asahi product which is very good, but a different look & feel to the original finish. Applying the new cover is very easy - the difficult bit is in ensuring you get all the old stuff off and have a clean, smooth, surface to work with.
I have no experience of Camera Leather, some folks have said they can be slow in shipping, but it is worth the wait. The only option that even gets close to the original seems to be to send it off to CRR in Luton, who can apply a modern vulcanite in the same way that Leitz did all those years ago. The problem with that is that it is almost £100 ($200) and Peter is always busy, so I would be unlikely to get it done this side of Christmas.
Someone mentioned the collector / user consideration and I think this is the way to decide. I will probably go for a Camera Leather genuine leather cover (also for my Standard) and see how that looks and performs. If I'm not happy with the results, I can always fall back on re-vulcanising by CRR sometime next year. Either way will allow me to apply a repair to the body where the flash socket was, and hide it under a new finish 🙂
Don't know if that helps, but it helped me (like loosening a pair of tight shoes - ahhhh!) Sorry, just realised how long this post turned out - oops!
[edited a bunch of times due to my dyslexic keyboard]