So, first off, the calculation for this is actually pretty easy! You need 1700 to get all the chests, and since the most you can get per run is 600, through the use of a Synergy Character and a 3X exp book, assuming you don't change the synergy character, or your powerful character, you will be rotating your third wheel every three runs. This will ensure each run ends quickly enough to keep you from wasting all the 3X exp books you're gonna need, since those are frankly more valuable than potions.
So, removing the two necessary characters, it goes:
90 x 3 = 270
90=Number of Characters
3=Number of Runs per Character
270=Number of Runs to get all chests.
That's how many runs you need. No need to do it all at once, but that certainly looks daunting!
We can then extrapolate this into how many potions would be consumed in the process, and that is a much quicker equation, since they restore full SP each use, and from full SP you can do four runs. Therefore, each potion used are four runs.
270 / 4= 67.5 Rounded Up = 68
270=Number of Runs
4=Number of Runs per SP Potion used
68=Number of SP Potions needed (Rounded Up)
So yeah, you need 68 SP Potions to get all the chests for each character. You probably need a few less if you're pacing yourself between 30 minute intervals to build up the SP gauge effecently, but that's the ceiling.