I've done 2 of 3...HM and OV. The former 3 times, the latter once. If I were to do either again, it would be a trip starting in Onion Valley. For beauty it has it all over the trip from Horseshoe Meadow...and I've done the both the Cottonwood Pass and NAP verisons, if this is your choice go over NAP or AP. I truly hate Cottonwood Pass.
My preference is for mid-September. I have done it in this time frame and have seen next no one between the pass and Lower Trail Crest. I true wilderness experience for a few days. You just need some warmies...we saw single digits on the summit one time and below freezing the other times.
I have done OV in 4 days and HM in 3. These are high paced trips. They can be done much more leisurely pace. The only thing recommend is not to stay at either of the east side ghettos. Either come out or stay at Consultation or Lone Pine Lakes.
Permits are generally not a problem for the trailhead and only a minor annoyance for the Exit...Trail Crest Permit. I never come out on the date of my permit. When I have been on a reserved permit, we take whatever date is available...no more than a week out or whatever is available as a walk-in. This process is made for lying and cheating.
No stinking lottery, period. Just call 6 months in advance of your entry. You will be in like Flynn.
The one time I did as a solo, I thumbed a ride over from WP to HM. Just park your car in the long term parking area at WP and make sure it is clean.