Weirdly enough, just using the tool instead of copying files with Explorer somehow stopped the weird hanging from happening, even without having to enable the actual throttling. Probably some bug somewhere along the driver/firmware stack triggered by the write block sizes.
Overall, I wish the drive vendors would expose some API to directly manage the SMR/CMR areas via software, just like the FLASH memory chips do. That would make the job of appending new backups + overwriting the old ones actually manageable with predictable and consistent timing.