Hi back and thanks for the update!
By looking at your schedule she does not seem to be facing overtiredness, she has healthy sleep habits so all this waking at night must be teething related. The pain is sometimes so strong that chewing is the only way to soothe it for a while so that might be the reason why the bottle is the only way to get her down and back to sleep.
Talk to your ped about this and see what s/he has to say about this. Teething her 3rd molar means she's almost at the end of this phase, but she still has one molar to go and the eyeteeth if they're not out yet (and they're also trouble makers, i can guarantee you). Talk to her about teeth and pain during awake times so she knows how to verbalize/sign it when it shows at night. Press the gums with your fingers or scratch them lightly and ask her if this hurts. Show her the oraljel (or any teething gel you use) and let her know it's the "special gum healer". Anytime she feels discomfort, she can get gel rubbed on her gums instead of a bottle.
Along with this, I'd suggest you to try and rub the gel during night wakings instead of offering the bottle. IF you're stuck with 3 bottles at night, try and cut one each third day. Instead of giving in and offer the bottle, try WI/WO (if you have the energy and stamina to hold on through the 2 hours of screams it will likely last) or gradual withdrawal (both described in the FAQ section). The first 2 nights will be the longest cause that's when you'll stablish you won't be giving in. If she's in pain, she gets the cuddles (short and brief) and the meds but nothign else. You wont' be leaving her to scream her head off, with both methods you're right next to her to keep her acompanied while she gets the grip on this, so she won't feel abandoned, and you won't be torturing her, just showing her a different way to deal with things. Keep this in mind as the screaming/crying lasts cause if you can hold on for 30 mins but then give in and offer a bottle, you won't be teaching her anything but "cry harder and youg et what you want". YOu have to be mentally and physically ready to try this for 2 long nights. After this, I think she'll slow down the night wakings but if she's too stubborn you might have to face a week of sleepless nights. IT will be totally worth it cause at the end you're gonna have a good sleeper and your nights back.
HTH and keep us posted!