Seems like it would work just fine on paper. I'm not sure about treating the channels as anything but unbraced, though.
Applying field welds from the flanges of the channels to the column seems pretty difficult in terms of access; particularly if they welds are full penetration.
I personally would probably push for the more expensive shoring/demo procedure and a more typical moment frame assembly, but that's mostly because I design masonry shoring pretty frequently and work with shoring contractors that are familiar with it.