As far as 3D printing, we haven't dabbled with it, but we have had folks come in to scan our objects, which is pretty cool. But we're also a small staff that doesn't have the time to really dig into the tech as much as we could.
Entry into this tech has become pretty cheap (a few hundred bucks for an entry level printer) and much more accessible in recent years. Maybe a volunteer/intern could help set you up.
Edit: NVM, I only just realised that was probably a _walk-in sized_ heart you're talking about. That's probably not gonna get cheap to produce anytime soon...