Leaderboards, a dig of the day, and what finds remain
The museum keeps a board now
Finish a twelve piece collection and your final museum score is calculated and it now goes onto the leader board, the score is deliberately not a time. It's the visitors your museum drew divided by the rounds it took. Digging a piece out carefully costs you nothing and the only thing that costs is losing a round, because a lost round is one more round for the same twelve plinths. So the board rewards care and punishes failure, and doesn't factor in rushing. A brass board in the hall carries the top five, and pressing E opens the whole thing, the top fifty, and your own place wherever it falls.
There is now a dig of the day. One seed, the same twelve corridors for everyone, with its own board for that day. Ring the bell by the arch and it sets your museum aside exactly as it stands, then hands it back when you're done. So trying it costs you nothing you've already built. Your best run of the day is the one that counts, so you can go again as often as you like. And the day after, yesterday's board is a keypress away, because the rank you see when you finish is only provisional as the day keeps filling behind you.

The wall above the tunnel tells you what you're collecting. Twelve carved places beside the entrance, one for every piece the museum can hold, in the order you'll dig them up. Each one holds a carved symbol of its piece — cold until you've secured it, warm once you have, whether it's standing on its plinth or out in the tunnel with you as a tool. Four of them are marked, because four of them do something.
Smaller things I've improved: hold crouch in the air and you'll slide the moment you land. The fallen beam past a pit sits further back, so landing the jump and getting under it is a fair ask. The hole a rockfall drops through is set into the rock properly instead of hanging under it.
The all-time board has current has my daily dig score on it. I don't think it would take much to beat.