Hi Miguel! I'll weigh in on this since I just finished a short tour of Skyline Drive and part of the Blue Ridge Parkway.
First, I'm afraid I'm not going to be much help on the logistics end. For my abbreviated route, I ended up just renting a car to Front Royal and renting a Uhaul back (I live in Charlotte). When I had originally planned to do the entire thing North to South, I could not find a way to get from Cherokee to Front Royal without enlisting the help of someone willing to drive me to Front Royal. At the end of the day I concluded that I would rent a car rather than try to convince my friends to drive 15+ hours round trip. The nearest rental agency to the start is in Waynesville (Penske). To get there from Cherokee you could take the Parkway (which would be a huge uphill climb even before you get to one at the start in Front Royal) and then exit at US 74 which I *think* would be mostly downhill into Waynesville. I believe there is a Penske in Front Royal as well. Sorry I'm not more help with this piece....
As far as parking goes...I thought of asking several of the local campgrounds if they would let me park there since I would stay a couple of nights before and after the trip. Harrah's Casino is also there and they may be an option (last time I was there they had a huge free flat lot...not sure if anyone would notice...).
Now for a few things I learned on my short trip. I severely overestimated my daily mileage. Having lived in the mountains of North Carolina and having biked and competed in triathlons there for several years I thought I could handle anything the mountains threw my way. Front Royal taught me a lesson over 10 miles and 2.5 hours of climbing. (And yes, I realize it was completely stupid to not just do a loaded trial run for a day climbing out of Asheville, hindsight is...). Coming from Florida I would imagine this is probably going to be your biggest unknown as well. I don't know what your touring background is but there are several very big hills on the parkway and Skyline drive.
I think as far as daylight goes, you should be alright in May. I did mine trip in October and there really wasn't enough daylight to go the distances I was going and still have time to enjoy the sites, the campsite, relax, etc. We had about 11 hours of daylight whereas I think you'll have about 14.
Second thing I learned was that because I had overestimated my daily mileage that I would have to venture off the parkway to get to camping facilities due to the distance between the NPS facilities. Because I was trying to alter my plans on the fly without cell service I ended up venturing off the parkway trying to find a campsite that ended up being closed. (I just couldn't do the stealth camping thing although I met a guy at the local camping shop who had no problem with it). In retrospect I would have like to have planned some alternative lodging and called to ensure they were still open. (Maybe I'll wait till the Skinner guide comes out with a post-Recession edition).
Third thing I learned was to be flexible with my schedule. I had fixed end date and I think that created some stress.
I also learned I packed too much food. Skyline Drive has a couple of places you can pick up camping meals. The parkway is a little less stocked. There is a town called Fancy Gap in VA where there is a post office less than a mile off the parkway where you could drop some food like you would if you were hiking the AT.
I will say this - Skyline Drive was beautiful. The weather was perfect. Saw tons of wildlife - bears, deer, raptors. The character is much different than the Parkway which is where I rode most of the time while living in the mountains. I loved being by myself and being about stop and look out over the valleys and see for miles - I've always found a sense of peace in that.
Let me know if you have any specific questions about things and I'll see if I can help.
