How do I force an iPhone to shut off with broken power button, unresponsive screen?

My screen is now unresponsive to touch, so I can't slide my finger to unlock. I am able to access assistive touch and pull the bottom menu up (with brightness settings, volume, etc) from the bottom, but I can't slide it back down. I found that this isn't an unusual problem, and I just have to force the iphone to shut off. However, my top menu button has been stuck for about a week and doesn't work. Even if I hold down the lock screen option in assistive touch and the power off screen appears, I can't shut it down because my screen is unresponsive. Waiting for the battery to die out would take days or weeks.

Is there anything I can do other than bringing it in? It's extremely frustrating.