After doing some testing today and rewiring my own chime box, I feel like I should post here to amend a previous comment:
I did it without any assistance after I took some time to think through the problem, do some other testing, and determine that the wire coming into my chime box and attached to the chime’s TRANS terminal wasn’t actually coming from the transformer. As I described in that other topic I linked above, once I determined the true transformer 2-conductor wire pair going into the chime box, I was able to test the AC voltage there with my multimeter and read 18.9 V AC.
I realize that your problem has been resolved for a while now. I just wanted to drop this here as an update in case it could be a helpful reference to someone else in the future.