Thanks for your replies-
I did get it to go in. I think the screw that's under the piston (and captive to it) wasn't turning with the piston. Since the pitch of those threads is so extreme, I LIGHTLY tapped the piston. Tap tap tap I must have tapped it a thousand times, and so instead of the screw threads turning and pushing the piston out, I reversed the process and turned the screw by tapping the piston in. I was very mindful of the small parts and the little ball bearing under the piston.
Parking brake works fine, pedal feels good. Thanks again for those replies.