Great Buy. Congratulations. I find mine really useful when working at a desk or a computer to work out lines, essential when I'm travelling, and just loads of fun at gigs when people can't believe that tone comes from "that little thing".
I never use mine with the body pieces now and have completely got used to it leaning away a few degrees on the strap: the bass I mostly play now is a Status with fret markers only on the side of the neck, so I suppose I don't expect to look at the front of the fretboard any more. Let us know if relocating the strap button makes a difference, just for interest though. I didn't try anything like that with mine because I didn't want to dig holes into that lovely piece of mahogany. (Mine was made in China, at least seven years ago, and the workmanship is excellent).
Incidentally, if you do try to find body pieces for your bass, I'm pretty sure there are two shapes, which may or may not mean two locations for the holes in the body where they fit. If you look at photos on TB alongside adverts you'll see that the E side piece is actually two pieces in one (more recent?) variation.