How do you handle dungeon-delving and getting lost effectively?
Honestly, I always assumed that if my jerkoff players can draw a map, their fairly competent characters should be able to do at least as well. Players hand-drawing their maps is a time-honored tradition and one that I would always use over the idea of some kind of a minimap you're suggesting. I think you might be missing another problem, by the way - while moving the overlay around, you'd inadvertently show some pieces of the map they have not seen yet.
My suggestions and experiences:
- Don't draw the map for them, just describe the rooms and corridors they're in. Make sure that you are not showing where they are, they need to come to this conclusion using both your descriptions and their drawings. This adds a nice element of uncertainty for the players, even if it usually doesn't do anything by itself.
- If they're in darkness/ running, or are otherwise engaged - cut the descriptions to the minimum and don't let them roll/ draw ("The footsteps are approaching! You're in a small room with worn-down statue, two doors, and a trapdoor. What do you do? You feel like you don't have much time before they get here!"). Actually, have some overpowering threat (that can be easily split into manageable threats for later) chase them at some point to drive them into a labyrinth of the tunnels. This should result in them only knowing where they are if they have a really good memory for directions and descriptions.
- Verticality, verticality, verticality. This is a megadungeon anyways, so it really should have more than a single level. Ceiling trapdoors dumping the party in already-visited rooms can make a mess of any player-drawn map. Underground it might be hard to detect that you're actually going down or up if the slopes are mild enough; so you might have them change levels without them knowing, or have them pass under or above another room. Changing levels combined with hidden passages gives nice strategic options when figured out, but can be used to make a mess of their sense of direction.
- Unwilling movement might be hard to include without teleports, but you can still use underground rivers, cracking floors and ceilings, uncontrollable elevators, sleeping gas traps and opponents seeking to capture and jail PCs.
- Also, have the environment change. Intelligent opponents might do a bit of quick masonry/ demolition jobs to add/ remove walls, but even some monsters might be smart enough to place a rock over the entrance to their pit when they leave. An encounter between warring factions can cover a room in a layer of blood and intestines. When you describe the gut-covered room to players, you can expect the reaction of "wait, have we actually been here?", especially if they got lost earlier. Then it is time for someone with medical skills to shine and deduce that this is all fresh-ish stuff, so maybe this is the place they know after all, just with a new coat of paint.
- A bit of an asshole thing to do is to ask which character is carrying the map around. If there's only one - have something set it on fire/ get it wet, or (somewhat milder, but still annoying) have an NPC steal it for later recovery. Overusing this might feel super cheap, though.
The natural reaction from players should be to start marking rooms they've been to with chalk/magic and perhaps even leave some advice for themselves for later, using ball bearings to detect inclines/declines and licking every wall looking for secret passages. This is great! All in all, if they are capable enough to make good maps, easily identify the room and be smart about the situation, they might never actually get lost. I'd advise against having opponents wipe their markings clean or making their tools suddenly ineffective - smart behaviour is to be appreciated.