Outside of the boss prize (Armos Knights), the vanilla big key chest (see Eastern Palace Big Key) is the slowest check in Eastern Palace, taking 50-58 seconds if checked immediately after the big chest.

Assuming the boss prize is required, an interesting situation arises if after opening the big chest, the only things that remain are one non-dungeon item and either the map or compass (happens 48% of the time overall). In this situation, the remaining item has a 50% chance of being in the big key chest and a 50% chance of being on Armos Knights.

The videos below show timing comparisons for going directly from the big key chest to the big door, going to the big key chest immediately after opening the big chest, and re-entering the dungeon to get to the big key chest after finishing the Armos Knights fight.

The exact approach you should take in this situation depends on what you want to optimize for.

To optimize for worst-case full-clear time, check the big key chest immediately after opening the big chest. This will prevent you from having to re-enter the dungeon for the big key chest if the final item happens to be there.

To optimize for full-clear time on average, proceed directly to the Armos Knights after opening the big chest, and re-enter the dungeon for the big key chest if needed. The time save from skipping the big key chest altogether is 50-58 seconds, and the time loss from having to re-enter the dungeon to get the big key chest (as opposed to getting it after the big chest) is 31 seconds, so you save about 10-14 seconds in the average case.

Of course, another option is fight the Armos Knights, and simply leave the remaining item behind in the big key chest if it happens to be there (i.e. if you "lose" the 50/50) -- saving 50-58 seconds over the worst-case full-clear route and saving 85-94 seconds over re-entering for the big key chest.

You will have to carefully weigh the pros and cons of each approach based on factors such as the current state of the seed, whether the big key chest is in logic, and your personal risk tolerance.

Note that the times above assume that you are doing a Save+Quit immediately after finishing Eastern Palace. If you instead want to mirror and exit the dungeon (e.g. if you want to flute away, or go to Sahasrahla), then the extra mirror and dungeon exit transition will cost an additional 4.8 seconds, reducing the average time save by half that amount. Of course, if you don't have the mirror on hand and elect for a death warp, that will take even longer, depending on your health -- an additional 12.6 seconds at the very minimum.