Need advice: Oblong space helmet from spherical acrylic

I am attempting to replicate a Mark Watney Martian-esque helmet visor for a custom space suit build. I have a 12" acrylic sphere with a 5 1/2" opening. What is the best way to reshape this into more of an oval/oblate sphere? My current thoughts involve placing it in an oven at low heat for a short amount of time, and pressing in on the sides after taking it out. I worry that the sides will simply cave in if I don't get the temp/timing exactly right. Is there a better way to do this? Additionally, should I cut a couple of darts in the obscured lower half of the visor to help with shaping? Any ideas are welcome. Thanks!

No experience with spheres, but to keep curves & contours in in acrylic tubing I used to keep a sprayer full of water on mist to freeze the acrylic in place.