Questions part deux...
Map...I've never pulled it out while on the trail. For someone using the trail, the best security blanket maps are produced by Whitney Portal Store, followed by Tom Harrison Cartography.
Acclimatization...Depends on the individual. Wifey can go up the same day, me, without drugs, more than two days.
Time...It will be more than your think in the best conditions and longer than that in May, if there is any snow at all around.