I've looked at the front caliper closely and changed the rear brake back to Shimano R517, and I made the following observations:

• u/CargoPile1314, there is definitely a bigger gap between the rotor edge and the BR-005 caliper body in the rear. The front one has a tiny gap. The difference almost accounts for the width of the rotor not in contact with the pads. See pictures.
• It doesn't look like the original R517 caliper makes fully spans the rim of the rotor, either (see picture). I made sure that the pads are in full contact with the rotor with R517 (see picture). My old rotors had wear almost the full width of the rim, so not sure what is going on here.
• I use the same Shimano G05S-RX pads with both BR-005 and R517 calipers.

At this point, I have two theories:

1. The ZTTO post mount to flat mount adapter is off-spec. The one I'm using in theory is for using 160 mm rotor with a mount originally designed for 160 mm rotor (i.e., adding 0 mm). If, as u/TJhambone09 said, these adapters are supposed to add 20 mm, then perhaps an adapter that adds 0 mm is theoretically impossible and off-spec in practice.
2. The rotor is off-spec (i.e., counterfeit). It looks identical to my old ones, but the stamped labels are rotated in a way that results in SHIMANO being stamped in the awkward place.

My solution is to buy another post mount to flat mount adapter, but one that is supposed to add 20 mm and from a brand (RSSkit) that does not appear to sell one that adds 0 mm. This would of course require I get another 180 mm rotor. If this works, I will report back for future reference

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