How do I reduce the risk of pinch flat punctures while riding up stairs on my hardtail?
I used to get snakebites like crazy doing urban riding, even running really high pressures. I'm a big guy. What finally helped was running higher volume tires and wider. See if you can fit a wider tire in your frame, and look at getting some wider rims. 

Increasing the volume of air adds more cushioning. As Batman mentioned, going tubeless also helps, since the tube displaces some of the volume between the rim and the tire.

If you're sticking with tubes, get some DH tubes. Normal tubes are around 1mm or less, DH are often around 1.5mm. They will weigh more, but might hold up better.