Sharkbite connection should work, you just need to find an adapter to step down the size to the small diameter RODI tubing. I have copper, not PEX, but the photo below should give an idea of what's possible. I found a push type step down fitting at Can Tire. I'd say most stores dealing in plumbing fittings should have something similar.
You definitely want to include a shut off valve so that the RODI isn't under constant pressure.
EDIT: Was responding while you posted the last photo of the metal fitting, looks like that should work just great.