So I heard from Iceoffreeze that he goes to door 1985 than 1980 and I wanted to know why. Did a little routing difference and here's my findings. (Note the parenthesis means that you have to go into that specific room to place items to get the key rings.)

1980 - Red Shoes > Vinyl > 0716 > Ring > [Bookmark Flower for 1985] 1985 - Doll > Book > Marble > Key > Luggage > Book > Flower > [Dump all clothing into Snake Wine pot for 1986] 1986 - Mei Shin's desk > Dress > Vinyl Player > Crown

1980: 1980 > 1986 > 1985 > 1980 > 1985 > 1986 (6 doors) 1980 > 1985 > 1980 > 1986 > 1985 > 1986 (6 doors)

1985: 1985 > 1980 > 1986 > 1985 > 1986 (5 doors) [Fastest Route] 1985 > 1986 > 1980 > 1986 > 1985 > 1986 (6 doors)

1986: 1986 > 1985 > 1980 > 1986 > 1985 > 1986 (6 doors) 1986 > 1980 > 1986 > 1985 > 1980 > 1985 > 1986 (7 doors) 1986 > 1980 > 1985 > 1986 > 1980 > 1985 > 1986 (7 doors) 1986 > 1980 > 1985 > 1980 > 1986 > 1985 > 1986 (7 doors)

If there's any additional routing that I could think of I'll edit the post, but for now it looks like there are 8 possible routes for the game with 1985 being the "fastest". I can't confirm since I've been only running the game for a week but I would think the 1985 routes could save a little bit of time.

Edit: 1986 routes are terrible when rerouting. Don't use them. The vinyl is a must needed item when you're going to 1986 and taking both the crown and the dress.

Therefore using the 5 door 1985 route is the fastest among all the routes shown.