You’re welcome, and thanks for the additional photo! 
Yeah, I’d temporarily nut the two red wires together just to stop the humming and unwanted doorbell actuations until you can get a Chime Controller—that is if you’re planning to get the Chime Controller so you can actually use your in-house mechanical chime; if you’re okay with not using the in-house chime, then you can just nut them together and be done with it.
If/when you receive a Chime Controller, then you’ll want to…
- Reconnect the red TRANS wire back to the TRANS terminal along with the Chime Controller’s red wire.
- Connect the red FRONT wire to the Chime Controller’s black wire with a nut.
- Connect the Chime Controller’s white wire to the FRONT terminal on the mechanical chime.
Basically, you’ll want it to be like the diagram in the Video Doorbell v2 Chime Controller Installation Guide.
Just to be sure that the current chime wiring is correct, you could also use your multimeter to test AC voltage across the terminals at the transformer and then test across each wire pair (one red, one white) in your chime box to see what’s a close match. That should tell you which red wire should be attached to the TRANS terminal. (That’s the thing that was previously wired wrong in my house.) Or maybe that’s what you’ve already done?
If this doesn’t solve the problems with your Duo Cam Doorbell, then I’d consider a transformer upgrade. I’ve had acceptable performance from my Video Doorbell v2 using a 16 V AC, 10 VA transformer, but since Duo Cam Doorbell is larger and has a second camera, it’s got more stuff inside, so you might find that you need more power. Also, there have been reports that the battery doesn’t seem to be adequately charging while the doorbell is connected to AC power, so that’s something else I’d probably keep an eye on.