I don't really fully understand the relationship between manufacturers DPI today. In the past it had a relationship with the dot pitch of monitors, but that is no longer the case, and I've always believed that the notional text DPI is more about the relationship of text to display than graphics.

Many modern display have dot pitches that are neither 72DPI or 96DPI, so I would give it a go at a much higher resolution.

I know my Mac has a notional screen size of 1440x900, but the monitor resolution is actually double that.

The slideshow will be of a specific size, so I recommend producing artwork of exactly that size and/or double that size. I think DPI is pretty meaningless for graphics used for display.