Having enough equipment is really the key to speed. My brew buddy and I have nearly the exact same setup, so I always have double the gear on hand. If you have a friend who can come by in exchange for beer, go with that. I find when brewing solo, that my mash time is usually just as long as my sparge and boil time. So if you're doing a mash in a cooler, you're going to have to wait for your sparge to finish before you can double back to start another brew. If you have only one burner, this can be a problem, too. I suspect that doubling your brew would add about 2/3-3/4 of the time of a typical brew session to your day. If you only have the one burner, I would recommend gathering your water for your second mash and heating accordingly, then start the boil on your first batch. If it mashes longer due to time constraints, so be it.
Oh, the things we do for beer. Good luck!