What's wrong with being thorough?

[Captain Kidd]

He's also provided us with practically unlimited resources... We've secured a large dining hall as our base, there is a kitchen with food, and we're constantly finding more food and drink around the dungeon (which we always drag back with us -- at this point our characters are happily filling their flasks with water and mead); from exploring so much, we've gotten a ton of gold that we've used to send allies into town to buy food and supplies when we're running low (whoever isn't in the active adventuring party gets to go run errands, and by the time we return our grocery list is filled). Our Bard and Rogue are always coming up with innovative little ways of getting other supplies and keeping us alive, as well.

So there isn't any reason for us not to take our time and explore. We're comfy.

This right here points the finger at him not you. If he wanted you to hurry up and get the adventure done, then he shouldn't have giving you such a base of operations and ample supplies.

He's got multiple solutions open to him, most of them fairly elegant and not too railroadish. He could have the monsters get wise to what's going on. Sounds like your group is spending in-game days there. At some point somebody surely has to be wondering why reports from that level stopped coming in and send in the bruisers to check it out. I'd even argue that, again assuming days are going by in-game, it's unrealistic for you to have had such free reign of the place. Unless he's set the dungeon up where the encounters are all predetermined and thus frozen in stasis until you enter that room, it should become apparent that somebody is killing off fellow monsters. If it's a free-for-all sort of dungeon, it's still doable. You're creating power vacuums, somebody should be attempting to snatch up all that suddenly available territory.

Another option is that you said the NPCs sent to check up on you are still with you. Did any return to tell the government? If not, now there's two groups gone missing; that should be quite worrying to the authorities. So one day you go back to your base and discover another adventuring party there, sent by the government. Now you're on a race with them to finish the job, winner gets the reward.

Edit: Oh, and when I said all that free territory, that includes your lair base. You return tired and exhausted to find that invaders have either trashed it, taking everything, or set up camp. Now you've lost off the loot you were storing there and probably are low on supplies. Said invaders could also be hunting you down. If you had such great loot for the taking, imagine what you must be carrying.

I avoided saying monsters because, if he was so inclined, the invaders could be another adventuring party. Maybe one not so inclined to team up; after all what dies in the dungeon stays in the dungeon with no authority the wiser.