efficient duplication of Time Machine backups to remote location I have been using both Arq and Time Machine for backup for years, but a year or so ago I got unlimited Google Drive space and decided to try making a remote backup (with Arq) of my Time Machine drive.

This may seem ridiculous, but it helps ameliorate a major problem with Arq: you can't move your remote backup from one service to another.  For example if you signed up for Amazon's drive when it was $5 a year for unlimited space, and used it for your Arq backups, and then decided not to pay $120 a year for sufficient space for your backups when Amazon said "oh, just kidding!" and changed their prices, you're unable to move your backup history to another location. (Since history is the whole purpose of a backup system, this is the one reason I no longer recommend Arq to anyone.  I used to enthusiastically recommend it to friends and family.)  Backing up your Time Machine disk allows you to have a remote backup that you can move from one service to another without losing any history.  (The only obvious downside is that you must first restore the whole Time Machine backup if your Time Machine disk has died and you want to change cloud provider at the same time.)

There is a non-obvious downside, however: Arq really sucks for this use case, for reasons I don't understand.  It gets through about 3400 GB (out of around 3600 GB) around the first day, then runs for days and days making virtually no progress, and then might at some point start to make some progress.  I don't know if I have ever seen it complete the backup. Many times I need to shut down my laptop before it completes.

I'd like to have an efficient way to backup my Time Machine drive to a remote service.  It can't depend on (e.g.) running rsync or Resilio Sync on the remote service.  

In case it's relevant for any reason, I have fiber, so the bandwidth is limited by the devices on both ends and any throttling the service does, rather than by the quantity of data pushed.)

One thing that Arq got right is the end-to-end encryption, so any replacement should include end-to-end encryption.  I'm not about to trust anyone with everything.
It is probably wiser to not backup the time machine backup, but instead make another backup of the computer directly.

The time machine format is a little finicky, as it uses a lot of tricks to save space while allowing to recover to many different dates, like reducing the amounts of dates one can go back to regularly. Even a minor corruption is likely to make it impossible to restore the backup of the backup to a functioning state. And that's exactly the situation you want the other backup for.

If instead you keep the backups separate, you have two completely different options to restore data if anything goes wrong, which should be useful in more situations.

Also, you can then use any encrypted backup solution you want.

Apart from that, here the official way to copy the time machine backup: https://support.apple.com/en-ie/HT202380

It suggests turning off time machine, then copying the backups.backupdb file to where you want it.

Note that this does not help with incremental changes, which is why I think it's not the best idea.

And here the closest to what you are looking for: https://www.berserkcomputers.co.uk/how-to-save-apple-time-machine-backups-to-cloud-services-like-onedrive/

In short, it suggests creating an encrypted image on your cloud drive with disk utility and then choose that as a backup destination.

Instead of copying the backup disk, just select two different disks, and time machine will use them alternatingly. This way, if one gets corrupted, the other should still work.

You can first copy the backup db to the image so that you keep the old backups, if you like. If your backup is already damaged, that will cause issues, though. If you have no likely need to restore an older version of your OS in the future, it's better to start a new backup, as the difference is mostly deleted files.