well all the keys as stated will not allow you to clone keys, except potentially the solo key hacker version and the tomu (hacker version if there is one), as the whole concept behind the 2FA devices is that you can't read the crypto keys off the device, if you could then a reader/device could grab a copy of those keys and your 2FA is no longer secure.
probably, however i only know about the solokeys hacker as that is all i own, and even with that what you would want to do is modify the bootloader to only update with your own crypto keys that you then keep in secure offline storage.
As far as i can tell there is not documentation on how to do this but the 5min look i had at it made it look quite easy.
Do the 2fa services you are looking at using allow multiple keys to be configured per user? if so that would be a much better way to do it than cloning keys. they would still have their backup but there wouldn't be the same security issues that are apparent in the process of cloning the keys. If the computer you used to "clone" the keys had been breached prior to you cloning the keys then someone could theoretically find all your 2FA keys and your 2FA would be useless
Mmh, I don't have any specific service in mind.
Concerning cloning, it's not such an important request, and if people have good reasons to think it's not worth it, I'm OK with that.
What was your experience with the solo keys, then?
I gather they haven't implemented SSH and GPG key "management" yet: is that right?
So for now it's just U2F it seems.