Bardic Inspiration can bolster saves. I tend to use it more for Cutting Words. There are only four per Short Rest. Given the parameters of the encounter with the time limit, we will likely get one, maybe squeak out two, short rests. We'll play it by ear.
If Flamestrike runs White Plume in the spirit of it, there should be a few puzzles that shouldn't require serious resource expenditure if we are able to figure them out. We will see. I'm assuming he plans to use some antimagic at some point given that is a commonly used tactic in tests of this kind. That will heavily hamstring us.