Can a surface mount Spa Panel be recess mounted in drywall and 2x4 wall?
You are treating a "spa panel" as something special when it really isn't.  Considering this is indoors, you can get away with a standard indoor breaker enclosure (NEMA 1) instead of the weatherproof (NEMA 3R) "spa panel" box.  In addition, the spa panel looks to be designed solely for surface (not flush) mounting -- flush mounting may cause issues with the door, for instance.

I would get a standard 125A main lug indoor panel (your existing spa panel uses GE THQLs, so get a GE panel if you wish to reuse the breakers from the spa box) and configure it as a subpanel instead -- while your current setup complies with Code insofar as you're able to get access to the junction box with the conduit body hanging off the front, I agree that it is a rather ugly kludge.