I wonder if there isn't an easy way to automate the parabolic flight - the autopilot should be clever enough to do it by itself without needing human intervention.
The real question is "does it cost more to certify the autopilot to do this than it does to pay for an extra two pilots", and with my understanding of aerospace costs that answer would be "very, very much yes".
I bet it does. Parabolic flights aren't really a huge market.