Video Doorbell 2 causes buzzing at chime

Two days ago I noticed a buzzing noise coming from our doorbell chime. I found that one of the chime strikers was vibrating quite a bit causing the buzzing. The Video Doorbell 2 was working fine. The rear doorbell (just a button) worked but would sound strange if you held down the button. I assumed it was a bad transformer (original to the house, 30 years old) so I ordered a doorbell kit (chime + 16VAC-10VA transformer). Installed the new transformer tonight, turned the power back on, still buzzing. I guess it's the chime? Power off, replaced the chime, power on, still buzzing (but quieter, probably the new chime). Voltage at the chime is ~16VAC. With the Video Doorbell 2 connected, I'm seeing \< 5VAC at the Ring device. With the device disconnected, I'm seeing ~18VAC at the wires and there's no buzzing. I'm assuming there's an internal fault in the device that's causing an issue. It was purchased in October 2019 from Woot as a used device. It appears to have just been an open box because it was flawless and still had all the protective plastic attached. Has anyone had something like this happen?