You are buying a reservation at rec.gov, not a permit. You have to complete the transaction the Inter-Agency Visitors Center in Lone Pine the day before your hike or make arrangements for pick up in the drop box.
On May 18th, you are heading into winter up high. Do not expect temperatures to get much above freezing during the day on the summit, last year the high on the summit was ~34 F on your date.
As for time, if you are safely geared up you pack will be approaching the mid 20#, add this to the slower pace due to elevation and the snow and ice you will most likely have to deal with, your time will be will be slow. Figure less than 1 MPH once your reach solid snow coverage.
I would suggest an much earlier start. Something that get you started up the chute at dawn and back to it before shadows are covering the glissade run...say 1 to 2 AM.
