We have an FS5-II but use ProRes RAW to a Shogun 7. The benefit of ProRes RAW is it's just like ProRes -- plays in Finder, roughly same size as regular ProRes, no conversion or transcoding required, and is fast to edit. Some short ProRes RAW test clips from an FS5 and Shogun Inferno can be downloaded from here:
I realize you were given the Sony RAW SQ files and must deal with those. This situation illustrates the benefit of a standardized RAW format vs a camera-proprietary format.
Despite these advantages, I am still not totally convinced if ProRes RAW is worth it, vs regular ProRes. My team is doing a lot of testing on this using the new A7SIII. Since we already have and use several Ninja Vs, we essentially get ProRes RAW for free -- it's just a config option on the camera and recorder. However (as implied by RAW) it is totally unprocessed and tends to be a bit noisier than regular ProRes, requiring more use of Neat Video in low light shots. It cleans up very nicely but Neat Video is a performance hassle. I'm also not convinced that HSL masks are working correctly on ProRes RAW, but I have more testing to do.