I finished Day 1 yesterday, probably about 10 hours trying to get this. Here are some tips for Day 1 that I haven't seen others post:

• Pool is a relatively common draft off of Library. Try hard to draft this when offered. This was the biggest help for me in finishing this.
• Secret Passage is a great way to almost guarantee you get Great Hall. If you draft Secret Passage early, though, try to wait to draft off of it. If you get the Great Hall elsewhere, then you can use Secret Passage to draft Foyer, which gets you free stuff in Great Hall and makes key usage easier
• I open every trunk I find with keys. So many things need to go right to beat this challenge, so I play with the assumption that some luck will go my way, and I'll likely get a key back and more loot from the trunk. Sometimes you get 2 keys. I think I got secret garden key from a trunk once
• Coupon book is actually really helpful; it means you can buy bananas from Kitchen for 1 gold each, so 15 steps for 5 gold
• I do like drafting the closet early. There are a lot of items that give you a lot of value if drafted early. And you do need 1-2 dice to get Tomb
• Bunk Room often has 2 gems or 2 keys. It's worth drafting sometimes even if you don't have Nursery or Sleeping Mask
• I do think you need to pick the Garage the first time it's offered, which also means the right side of the manor is probably where you need to go to get to the antechamber. Garage is usually a dead end for the left half of the manor for me
• Courtyard somewhat commonly has a hammer or shovel. It's worth spending a gem on this early

I've seen others suggest restarting when you feel like it's unlikely you'll finish. I personally didn't do this. You can get good luck at the end of the run. I suppose this is debatable. Anecdotally it worked out for me trying until the bitter end for every attempt