Came across a bug. Apparently it's possible for Tinelli's gem to not drop. I had thoroughly explored everything prior to the bridge so I didn't miss her, but her gem wasn't in my inventory. Using a save editor to force it in and try to fix it, the bridge still would not register that it was in my inventory and open up.
In that particular run, I had just broken all of the illusion gems rather than looking at any. This may be what messed things up but I can't tell.
Viewing post in Kilgor & the Succubus World comments
I will see if that's in my inventory next time I'm on my clean run. I will let you know if it's not, somehow.
Slightly more concerning is the fact the blue orb wouldn't activate even though I had the item in my inventory. If only because it meant it was difficult to attempt to fix a potentially more serious problem.
EDIT: I did overlook the necklace drop that included her orb. Now have 2 and the bridge is properly unlocked now.
Now I've come across another bug though. If you get both the Rematch and Recollection room in your Jimeng Home, and enter the Recollection Room (which will have everything unlocked, btw), it'll unlock all of the fights in the Recollection room.