When I re-read your post and thus remembered you were doing a 5-pounder I thought you may have missed it's high point because that many hours at the temps you were running is excessive to me. I think Paul might have been thinking along those lines too when he suggested repositioning your therm. It's possible you hit your temp without noticing (perhaps some time before you ran out of fuel?) then, with the extended cook time,it dried out. Though butts in particular can take higher heat, judging from your description of the cooked butt it cooked too long. Note though that it is possible for the meat to overcook without hitting your target temp. If it goes too long the moisture is going to evaporate out. You can end up with meat that's neither tender nor juicy, as you say.
I would definitely agree that there was a problem in letting the cooker get to 300 before you put the meat on. Butt, like I said above, can take higher heat (and can be cooked at a higher heat successfully), but variables change if you do so, especially your ability to control the cook, imo. (Running out of fuel is case in point.) I think a gentler cook is easier and more forgiving, especially with butts as they are fairly forgiving on their own.
Next time: Start with a full ring and 15 or so lit coals. I spread my lit out, some put all theirs on one side; some all in the middle; your choice. Put very hot water in your pan; assemble; put on your meat. When your lid temp nears 200 start closing bottom vents. Everyone has a different preference here depending on circumstances and taste but I close the windward vent all the way and the other two 2/3 closed. (This depends on weather and ambient temps.) Your temps should continue to rise slowly; give it 20 min to see the flow. Open one or two slightly more if your temp stalls or the rise slows dramatically; close slightly if the rise is fast or you overshoot 250. Try getting to 240-255 or so, somewhere in there; once you hit a spot in that range and it's stable there, you're fine. Remember you need to allow 20-25 min for a vent adjustment to be fully realized so be patient. If you need to close the bottom vents all the way don't worry about it. If you don't start with too much lit you probably won't but it happens sometimes like on windy days (a good windblock is a good idea). If you can keep your top vent open your cooker will be fine even if you have to close the lowers to keep your temp where you want it. You will want to watch things though, after the coals do without much air intake for a while, you'll likely need to open one or two slightly.
The rub should taste approximately the same after chilling and re-heating, though this depends somewhat on the moisture left in the meat, whether or not you chill with any added liquid, and whether or not you add any liquid for the re-heat. (Chopped butt scrambled with eggs and cheese and onions is great for breakfast.)
You obviously have thought about your first overnight cook and learned a lot from it which is great. And you have cooked butt, perhaps not exactly the way you wanted it, but cooked, tasty, and useable nonetheless. Add some moisture (and perhaps a touch of fat) during the re-heat and you're good to go.