This has been discussed piece meal already, but as I missed those discussions and messed up the side quest, I wanted to try to simplify the SQ for those that haven't completely screwed up yet. This is my current understanding of the SQ, so of course I could still be wrong, but I hope this will help some people, and I wanted to highlight not just where I screwed up, clarify how to avoid messing up like I did.
Here's my simplified instructions for the Side quest.
Every week there will be a four part objective to earn Maze keys. This week it was the one to defeat Defense:Tank champs with mutants. You can earn four Maze keys from this objective.
These keys should be used in the Maze map to earn Vault keys. Here's the part that bit me. YOU ARE NOT INTENDED TO EXPLORE THIS MAP. This map has optional paths to reach the keys. You are supposed to grab four keys from this map that are at the ends of four different sets of optional paths. Specifically:

You are supposed to head in each of the four directions indicate by the red arrows ONCE. In each of those directions is a vault key. If you go in any of those directions more than once, you will burn a Maze key but not get a Vault key, because you already got the vault key in that direction.
Vault keys are intended to be used in Vault maps, and there will be four Vault maps, one per week. In theory, you can use the vault keys any way you want, but for each difficulty tier there is a corresponding objective: the "chessmaster" objectives:

The only way to get any of these objectives is to fully explore all of the vault maps for that specific tier. There are four vault maps, each takes four paths to explore. Four Maze keys per week, if each earns a vault key that is 16 vault keys total. So there is only one way to get exactly one of those Chessmaster objectives. Earn all sixteen maze keys. Use each Maze key to earn sixteen vault keys, without missing a single one due to a Maze error. Use each vault key to run one path in a vault, and use all sixteen vault keys on sixteen separate paths in four vaults ALL OF THE SAME TIER. There is no wiggle room, and no margin for error.
I interpreted the announcement incorrectly, so I'm already out the chessmaster objective. But that's not the end of the world, I'll still try to optimize the rest of my run through. But for those that haven't made that mistake yet, and aren't yet fully sure how the quest works, this is my best understanding of it and how to run it properly. If anyone has any corrections to this, please post here and let me know.
PS: What was my error? There's a "THE MAZE" map and "ROOK'S VAULT" map this week. I assumed that there would be new vault maps, one for each vault type (ROOK, KNIGHT, QUEEN, KING) but it did not occur to me that there would also be new MAZE maps, because it was called "THE MAZE" and not something like "ROOK'S MAZE" or whatever.