The original game features a ton of game-breaking glitches (shout-outs to swimfan for finding them!). Some of them work on the remaster as well.

Thanks to these glitches, there are currently two possible routes we can take to beat the game as fast as possible. Their main difference is who gets certain items in the present. In particular, the gun and stamp. We don't know which one is faster - they seem pretty close.

Route #1: Hoagie gets the gun and the stamp

1. Unlock Hoagie. With Hoagie, get the soap.
2. Switch to Bernard. Get the keys, look at the TV in the honeymoon room, the fork, the decaf, the coffee, and the funnel. Flush the book to Hoagie.
3. Switch to Hoagie. Get the wine, the fake teeth, the red paint and the mouse toy.
4. Enter the window to go to the roof and, right when Hoagie's left leg is making it through the window, switch to Bernard in order to get the Hoagie Hustle.
5. With Bernard, open the grating, start walking towards the salesman, and flush an item to Hoagie (this will be your second flush overall, which starts a cutscene) at the same time you trigger the salesman cutscene. This way you'll get the item slide state.
6. Give the keys to ski mask, and start walking back to the motel during the cutscene.
7. Use the crowbar with the candy machine, and pick up the quarters.
8. Get Hoagie to the present thanks to the quarters cutscene.
9. With Bernard, go to the basement. Then, get the contract with Hoagie using the coffee cutscene. Get the bankbook and the Booboo-B-Gone.
10. With Hoagie, get the gun. You won't need the letter; Hoagie can walk through walls and so he can freely enter and leave the room.
11. With Hoagie, get the ink, push the speaker, use the stereo, get the stamp, get the crank. Flush the contract and the gun to Bernard.
12. Enter the chimney with Hoagie. You'll see Bernard going down the chimney and getting to the living room. Click on the door and Hoagie will make it to the lobby.
13. With Bernard, switch the guns, get the cigar, get the chattering teeth. Flush the lighter and the cigar to Hoagie, and go to the lobby.
14. With Bernard, start walking to the dark passage. While Bernard is walking, switch to Hoagie, pick up the fake barf and the help wanted sign, and start walking to the dark passage too.
15. Switch to Bernard, and enter the dark passage.
16. Switch to Hoagie, enter the dark passage, and start walking to the left. Switch to Bernard and give the decaf to Dr. Fred.
17. Walk both Hoagie and Bernard to the leftmost end of the basement, and quantum-swap the plans. Skip the cutscene and Hoagie will go back to the past.
18. With Hoagie, paint the tree.
19. With Bernard, use the funnel and the coffee with Dr. Fred and sign the contract. Flush the contract and the chattering teeth to Hoagie. Walk next to the clown and leave Bernard there until Laverne flushes him the scalpel.
20. Play the rest of the game as normal (except for skipping the hamster) until Laverne makes it to the basement in the future.
21. Use the Hancock conversation with the canary to use the hamster in the future.
22. Play the rest of the game as normal.

This run was first used in my 13:15 run.

Route #2: Bernard gets the gun and the stamp

1. Unlock Hoagie. With Hoagie, get the letter and the soap. Flush the letter to Bernard.
2. Switch to Bernard. Get the keys.
3. Give the letter to Dwayne, get the ink, look at the TV in Dwayne's room, get the gun, push the speaker and use the stereo.
4. Get the stamp, get the crank, go down the chimney, and open the grating.
5. Start walking towards the salesman, and look at the stamp (which starts a cutscene) at the same time you trigger the salesman cutscene. This way you'll get the item slide state.
6. Switch the guns and, during the cutscene, start walking towards the kitchen.
7. Get the fork, the decaf, the coffee, and the funnel. Flush the gun to Hoagie.
8. Give the keys to ski mask, and start walking back to the motel during the cutscene. Pick up the fake barf and the help wanted sign.
9. Switch to Hoagie. Get the wine, the fake teeth, the red paint and the mouse toy.
10. Switch to Bernard. Use the crowbar with the candy machine and pick up the quarters.
11. Get Hoagie to the present thanks to the quarters cutscene.
12. With Bernard, go to the basement. Then, get the contract with Hoagie using the coffee cutscene. Get the bankbook and the Booboo-B-Gone.
13. With Hoagie, enter the dark passage, and start walking to the left. Switch to Bernard and give the decaf to Dr. Fred.
14. Walk both Hoagie and Bernard to the leftmost end of the basement, and quantum-swap the plans. Skip the cutscene and Hoagie will go back to the past.
15. With Hoagie, paint the tree.
16. With Bernard, use the funnel and the coffee with Dr. Fred and sign the contract. Flush the contract to Hoagie.
17. Go to the living room, get the cigar and the chattering teeth, and flush them to Hoagie.
18. Walk next to the clown and leave Bernard there until Laverne flushes him the scalpel.
19. Play the rest of the game as normal (except for skipping the hamster) until Laverne makes it to the basement in the future.
20. Use the Hancock conversation with the canary to use the hamster in the future.
21. Play the rest of the game as normal.

So far nobody's used this route in a run.