That would certainly provide clearance for the RTC by mounting the fan sideways.

I guess the only question would be whether the displaced fan would give adequate cooling to the main chip.

This would be a minimally invasive way of getting what I would need, thank you for suggesting this.

I spent a couple hours searching online for a Pi case that was tall and included a fan and came up fairly empty, with only a couple plausible solutions.

It would seem that I would not be the only one looking for a little more clearance in a Pi case.

Another possible solution would be finding a RTC that didn't mount directly on top of the pins.