Since a saved game saves whether or not a treasure has been opened, there must be a place in the first 0x1800 bytes of RAM that stores which chests have been opened (because that's what a saved game saves).
It's
probably a block of 0x40 bytes (256 bits for Overworld, 256 for Underworld/Moon), and works a lot like event flags (when one is opened, a bit gets set). If we could find this, then you could manually reset all chests in your save in order to test out the chests in your challenge dungeon.
OK, so... there's a couple of things I'm looking for this morning.
I'll get right on it.

OK, well, treasure flags were super easy to find. They're immediately after event flags - 7E:12A0 - 7E:12DF.
Set this whole string back to 00s and all of the treasures in a save will be unclaimed again.

2 You're mostly right about the problem with extra maps being lack of space, unfortunately. Map formation pointers are at B8000 (or B8200 with header) through B82FF, and map formation data is B8300 through CFE5F.
CFCF9 through CFE5F is empty, but that's not a whole lot of space for a map - 358 (dec) bytes, or about enough space for 3 fully furnished 10x10 rooms.

You'd also have to have the (Underworld/Moon) flag set in the map properties to have your map load from this part of ROM - not really a problem, but an extra thing to consider when setting up NPCs, treasures, and various other elements that use different indices depending on Overworld/Underworld.
Now, because FF4kster condenses data banks to eliminate wasted space, a ROM edited with FF4kster may have a bit more space than a vanilla ROM.
Let's see...
Nope. Looks like this is actually one place where Square was pretty efficient with their use of space.

Well, you know what we're gonna hear eventually from somebody if we don't preempt it: "Why don't you just expand your ROM and point to the newly-created larger space?"
That, unfortunately, does seem like the only solution that does not involve destroying or shrinking other maps, but you know as well as I that doing so would cause FF4kster incompatibility, which would sort of defeat its own purpose.
So you are stuck with the following options (as I see it):
1) find some locations that you don't need at all. The forest clearing after Rydia summons Titan comes to mind - that event could easily happen in the chocobo forest index, or, you know in a field background since there's no forest there anyway. The place in the ending where Palom is bragging to Leonora - isn't that a unique location? Well, you're much more adept at finding superfluous usage in the game than I am, but the point is - it does exist.
2) Shrink some locations' data footprints by removing what doesn't need to be there.
For example, if you take the Baron Weapon/Armor shop and remove the empty chest that's in a different Y location than the rest of them, all of the wall decorations except for the Sword, Shield and the torch in the center, the pots, table and chairs in the bottom corners, and the stools in front of the counters (replace with blank counter front), the map goes from 166 bytes to 149. Seventeen bytes isn't that much, but doing this with 256(-ish) maps could free up a lot of space.
Hey, blanking out the entire top half of the Bab-il crystal room frees up 255 bytes! Just removing the "edge" of the top, left and right of the oasis in Kaipo, which you never see (replacing it with "center" water tiles) - 31 bytes!
So this idea, while it would take a VERY long time, definitely has some potential...