Well, the issue is that choice 1 in the NW shrine initially is to unlock the apartment. Then there is no choice 1, until you get the sphere.
What I'd done was to set the shrine to unlock (choice 1 always). However, on adventuring at the NW shrine (adventure * shrine northwest) it kept trying to burn adventures after it was unlocked and nothing was available.
My hope was that it would just unlock it and stop... similar to an autostop, I suppose. Not sure if the r12599 choice handling makes it work similar to the special Bedroom unlock handling from a few years ago where you can have it pick the right drawer automatically during automation, but since it doesn't take a turn, without forcing an abort it would run forever.
Now in the choice manager you have two options :
1. Show in browser
2. Do unlock hidden apartment building or get stone triangle
If you pick the second, it'll unlock on first visit, get stone triangle if you have the moss-covered sphere, otherwise show in browser.
If you want to automate, you want to set a (default) goal of 1 NC, run turns at NW shrine with choice of "unlock hidden apartment building or get stone triangle", then set a (default) goal of moss-covered sphere, and run turns at Hidden Apartment Building with choice of "fight spirit or get cursed", then run turns at NW shrine with same goal and settings.
It's not optimal, but if you set appropriate choices and default goals, you should be able to complete quest with :
adventure * overgrown shrine (northwest)
adventure * hidden apartment building
adventure * overgrown shrine (northwest)
adventure * overgrown shrine (southwest)
[hidden hospital requires equipment changing, so not trivial]
adventure * overgrown shrine (southwest)
adventure * overgrown shrine (northeast)
adventure * hidden office building
adventure * overgrown shrine (northeast)
adventure * overgrown shrine (southeast)
adventure * hidden bowling alley
adventure * overgrown shrine (southeast)
adventure * hidden ziggurat (southeast)
Edit - Hmm, I should really add a default goal of 1 antique machete to hidden park.