Rather than having PCs navigate over the GM's reference map, it might be useful to have them navigate the dungeon as a node graph - an abstract map of rooms and their connections, which doesn't have to be any more complicated than a bunch of ovals and lines, with unconnected lines representing passageways the PCs know about but haven't taken yet.
4E doesn't pay much if any attention to specific distances outside of combat proper, so navigating a map abstracted in this way provides the PCs with a workable overview of the dungeon and its structure without needing to make an entire grid map navigable.
When it's time for a fight, you can draw the immediate terrain on your battle map and mark out some squares as an allowable deployment zone based on how the encounter started and on what terms. If the PCs are surprised you could forcibly split the party by having multiple deployment zones, none of which are big enough to hold the entire party, or you could create a large deployment zone but not put down most or all of the monsters until the PCs have finalized their initial placement.
This lets you give the PCs the sense of a large place with many unexplored passages, lets you keep secret doors a secret until they're found or, perhaps, used to your advantage, and still restricts initial placement on the battle map to something sensible.
If the battle starts to move too far off the edge of the map, perhaps because the PCs or monsters are trying to run away, it may be useful to break off combat and into a skill challenge (difficulty depending on how outnumbered the running side is) about trying to run down the fleeing monsters or to escape unscathed.