If you have some flexibility just get walk-in permits for the next day. You might have to wait until the "day after tomorrow", which is a sure bet, but I have only missed on a "tomorrow" permit once out of about 9 trips (all 8 to 11 days). This is especially true if you stay out of the BA corridor.
Get the Sky Terrain map with the Travel Zone designations to see how to plan a trip. Go into the BCO in the afternoon and chat with a Ranger. Explain what you want to do, what a "long day" means to you, learn the walk-in rules, and have them run an itinerary to see what might work. Then go home, make your plans, call the BCO in the afternoon, and have them run That itinerary. If it works, show up the next day and do it in person. If it doesn't, ask them what would work. They are a great group of folks who know how to have fun in the Canyon.