OTP sequence uniqueness
Yes, it is possible.  You described how in your question.  I'm not sure what your remaining problem is.  You can think of this as two totally different, independent logical "users" -- or as two different OTP sequences -- with both of them assigned to the same person, using a different one for each channel.  If the OTP scheme is secure, then your approach will be secure too.

The difficult part will be the usability aspects: to convince the user to make to use the proper OTP sequence for the channel they are using.

Also, OTPs are not secure against man-in-the-middle attacks, so they are not a complete solution.



Lastly, one tip for how to get better answers here.  Try describing what you are trying to achieve (what your requirements are) and ask for how to achieve it.  You might get answers or approaches that you hadn't anticipated.