Dr.
You asked for advice but did not provide any of the considerations that are important to you. If you leave W-E in May you will see snow in the air and on the road. But many folks do that and are ok with it. Certainly it will be warmer in the east if you go W-E than if you go E-W, but many folks do that and are ok with it. All depends on what you want. If I had other considerations that dictated my riding W-E then I would probably opt for the Aug departure. Good luck with your ride.