(Moved this from guides as I'm not 100% confident I have this correct yet.)
I spent most of a day running trial and error for certain times and frame windows for the several potential time-saving ? options for travel: Hillsfar - Rock Quarry, Big Tree - Hillsfar, Hermit's Place - Hillsfar, Ruins - Hillsfar, and Rock Quarry - Hillsfar.
Of these only three actually had the potential to work in favor of the run (Cleric route): Big Tree-Hillsfar, Hillsfar - Rock Quarry, and Rock-Quarry - Hillsfar.
Where you end up seems to be linked partially on the time of day in-game it is, but it's more specifically to a window of frames since frame 129 after a reset or power-on. Every 8967 active frames game time advances to the next hour. A handful of frames can be lost from events like a thief approaching you for a job in Hillsfar.
I initially tried each one based on the time of day, 1 - 12 (AM/PM didn't seem to matter). This gets obscured somewhat from resting, as the destination of the ? paths still seem to be consistent with what time it WOULD be if you hadn't rested opposed to what time it IS since you've rested. The run's short enough that if you never rested it'd be between 12-1am in game.
What's great is the return route from the Quarry to Hillsfar only works at 11 and 1. That lines up nicely to when it's usually possible to get TO the quarry with the quest. The hope is to leave the quarry inside of one of those two 8967 frame windows, which could be as much as 1000 frames delayed depending on progression and events. That's mostly why it felt like it was 50/50 when I was initially testing this return trip with save states, I had the state saved right on the border of these frame windows.
The game starts at 2pm. So your windows (Frame-wise) for a successful trip from Rock Quarry to Hillsfar are frames 80833-89799 and 98767-107733 (again these will be affected by dead frames). My 30:34 run exits the quarry at 102973, comfortably in the latter window, so I got the trip back to Hillsfar.
Similarly, you have three windows (or one large window) to get to the Quarry from Hillsfar on the 1st of the ? options between frames 80833 and 107733. My 30:34 run left 88831.
The shortcut I didn't use in my run that was the only viable one for Cleric I found was Big Tree - Hillsfar. This one works (relevant to the run) from 2-4 or frames 130-27030. This is a time save of almost 2300 frames, or a bit over 38 seconds, from going to the trading post then Hillsfar, assuming no falls on the treck to the trading post. This is using the three inputs ? path. My 30:34 could've used this as it left the big tree at 12120, well under 27030.
A concern I had was using the Big Tree - Hillsfar shortcut might cause the trip to the quarry to be too soon to work, or worse put the return trip at risk. It might be possible it could, but it's not likely in most cases I feel.
So, in summary, there are three shortcuts to use:
#1: Big Tree after finding the Acolyte: use the 2nd ? option (three inputs) and it'll take you directly to Hillsfar.
#2: Hillsfar after getting the quest to go to the Rock Quarry: Use the 1st ? option (four inputs) and it'll take you directly to the Rock Quarry.
#3: Rock Quarry after finding out Darhma's hideout is the Haunted Mansion: Mash A-button after leaving the quarry to get into the riding section. It'll take you directly to Hillsfar.
#1 should work 100% of the time so long as you exit the tree before frame 27030.
#2 should work if you leave Hillsfar between frames 80833 and 107733. A little later might work depending on how many dead frames (where the internal clock doesn't tick) you had during the run.
#3 should work if you leave the Quarry between frames 80833 and 89799 OR between 98767 and 107733.
If you're not on emulator (Everdrive/etc or actual cart) if you're loading a character to ride about as quickly as you can generally you'll start at about frame 1900-2000. 8967 frames is 2:29.45.
The Hillsfar-Quarry window is approximately 21:53.89 - 29:22.22
The Quarry to Hillsfar windows are 21:53.89-24:23.32 and 26:52.78-29:22.22.
