Good ideas! I was definitely envisioning the over-map as being a way to exert a bit of control over the style of level you play, in terms of what the level generator is and what play features are present on it. It'd be nice if the player could pick to a certain degree but with some surprises, still. Obviously I would need to develop more level generators and play features to get the variety.
The idea of making a district ramp up in difficulty is similar to one I'd had; it would help push the player to try different areas. Another idea along those lines was that I was thinking mansion owners could stay home or visit someone else's place each night, so you'd get some mansions that are lightly occupied but guarded, and others that are full of people, and which was which would change each night. The ones full of people would have goals involving information-gathering, and maybe disguise gameplay, while the ones with the owner gone would be more focused around stealing loot or documents, and maybe feature traps and alarms.
I'd like it if there were some gating so you can't just go straight to the final location, but I haven't come up with how that would work. I tried a variety of puzzle-ish games, looking for the feel of gathering clues that help guide where you go next, but I think I was going too complex. All those prototypes are not web-playable, alas.
It might be enough to just have a couple of tracks you need to make progress on: money and clues. The money track would be straightforward looting (and you can't really loot the same place twice), and the clue track might just pick a subset of the maps each turn, and playing one of those would give you a chance to collect the next clue. I think stealing information is a potentially interesting vein to mine: overhearing conversations, digging up records, confronting people when they're alone, that sort of thing. If/when I return to this I'll be trying out some mechanics around those.