Mike,
Your OP seems a little wish washy. You start out claiming you want “schedule flexibility” and poo-poo the 121 “iron grip” on your schedule, but then state your dream gig could include an “off/on schedule” like two weeks on, two weeks off? I’m not sure you have really defined what YOU mean by schedule flexibility.
I agree with [MENTION=93050]Ovenmitts[/MENTION] that Part 91 is probably the least “flexible” because you have to go when the owner/client wants to. If you don’t, you’ll be looking for another gig really soon. NetJets, FlexJet, and XOJET all offer fixed schedules (7/7, 8/6, 15/13, etc.) and flexible, biddable schedules. Even on a fixed schedule, you can swap with another similarly qualified crewmember to get particular days off, as needed.
Perhaps you could think about it more and ask us about what you REALLY want?