That wouldn't fix the issue, because it could be easily "cheated" due to how Palace of the Dead works. Speed through until the last two or three floors, which you clear out.
Rewards should instead pay out on a floor-by-floor basis, with extremely severe penalties inflicted on the player if they leave the dungeon early (for example, instead of just a flat 30 minute Duty Finder lockout, have a 72 hour lockout and 80% reduction to all other rewards across the rest of their gameplay during that time). Have rewards reduced for the rest of the party by 80% for the rest of the duty if a player is dismissed, to discourage vote dismiss abuse to bypass those penalties.
Instead of a linear scaling amount of rewards, just flat remove gil/tomestones and reduce exp payout by 50% if the floor is less than 50% explored. If the floor is at least 50% explored, and at least 50% of the base population is killed, then give full base reward for that floor. If players complete 100% exploration and clear 100% of base population, then triple the base reward for that floor, as well as increase the chances for positive floor effects and reduce the chances of negative floor effects on the next floor.
These changes would instantly remove speedrunning, and would make Palace more rewarding to run. It would also make future "Deep Dungeon" content more fun as well.
I put quotes on "Deep Dungeon" because I'm about 99.9% positive we're getting a "Tall Dungeon" in that tower in The Ruby Sea whenever they release the 4.x version of Palace. Not the only one who thinks this, either. That place just screams Palace-type gameplay, especially when you fly up close and examine the architecture more carefully (clearly split into floors, separated by what appear to be discs that could be the floors can be rotated around on... not to mention those Jenga blocks that could be rearranged to explain the random floor generation). Not to mention that it's clearly made by something other than the currently known races, being high-tech yet distinctly not Allagan/Garlean.