I do this, but the downside is, if I lose one I have to go through each service removing both tokens (because some services do not tell you which is which) then

I do this, but the downside is, if I lose one I have to go through each service removing both tokens (because some services do not tell you which is which) then adding the existing (not lost) token with the new one. This is making me wish for OpenID again where I nominate my authenticator of choice so I only have one place I need to maintain my tokens.