WHAT'S THE BIG PROBLEM WITH THE WICHITAS??
Assuming that the SOA had a rift-type crust in the Cambrian, there are basically three different scenarios to "add" the required 15 km or so: basaltic underplating, transformation of eclogitic mantle to gabbroic crust, or deformation (squeezing) by some large factor. There are no significant heating events, later than Cambrian, in the geologic record of the upper crust in the southern Midcontinent. Thus, both underplating and transformation of eclogite to gabbro seem to be out. That leaves deformaion. For this we can appeal to the Pennsylvanian Ouachita collision which will require massive compression in a very specific part of the lower, ductile crust.
Ultimately we are left with 2 broad questions: did older rifts originate as present rifts do (as assumed above), and how to change rift crust into platform crust. These have to be questions of general significance since the geologic record clearly shows that bigger plates (e.g., Rodinia, Pangea, Gondwana, etc.) get broken up into smaller, or different plates, with time---and this happens by rifting. The consequences of adopting a compression scenario should be applicable to a wide variety of geologic settings both in time and space.