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From the old device, I copied the backups to a thumb drive. For whatever reason, copying from thumb drive to /Android/media/com.whatsapp on new phone was not working. What DID work was copying the backup from thumb drive to the new phone's /downloads folder, then from there I was able to copy the backups to /Android/...
Problem now is that I'm locked out from Whatsapp for several hours, unable to transfer the account to new phone. Will try tomorrow, hopefully the backup will work. I'll report back.