Well, the neck blank being a bit thinner to start with might come in handy here. I read somewhere that I should at least have 3 mm of wood left behind the truss rod. That would give me a neck thickness of about 20.5 to 21.5 mm from 1st to 12th fret, which is what a Regius is according to the specs. Also, I have a custom Fender Strat with basically a baseball neck (1 pc maple of 21 mm all along the length) and that plays like a dream. So with the right curve, a thick neck is not really a problem for me. Overall, I'm pretty satisfied with this attempt, route being dead straight in the center and mostly at the correct depth.
Having said that, it may still be a good idea to fill that part of the route, for some extra stability. I'll check the radius of the bit and see if I can find a properly sized dowel.