I've just bought a SC Brown and was surprised it was neck heavy, particularly given the pedigree (and price). So I've gone for a wide (3.5" widest I could get easily) suede backed strap which helps a bit. I also dont like the tilt forward at the top (will try the arm placement recommendation). The strap I got is shorter than I'd like so it's also higher on the body, but that's not my comfort zone.Today I experimented with an extension of what Mica told me, that SC used a large washer and a wood screw and basically screwed the strap to the mount point, so now fixed to the guitar. I can see how this method would help as the strap angle isn't as flexible at its mount point anymore, and this flex is exacerbated even more using the strap locks which also move the strap further from the mount point. So what I tried was to replace the strap lock washer (which at that end is on the inside of the strap) with a piece of very stiff plastic (I used the little plastic hanger that the strap came with (to hang on the display at the shop) and drilled a 1/2" hole in it at one end to basically replace the washer and extend some stiffness up that part of the strap). It helped but is still too flexible (I'm trying to keep the strap end vertical). You could also try a credit card (or 2 if they'll fit on the strap lock), it's also not ideal that the plastic isn't fixed to the back of the strap at its top end. Better would be a piece of metal with a 1/2" hole drilled at one end sandwiched (securely) inside the strap end extending about a credit card length from the strap hole up the inside of the strap. This will stop the strap bending (as leather does) and keep a more vertical angle, sort of the essence of what SC did (well in some ways).
Anyway my 2cents worth so far. Apart from this, the bass it just a beautiful joy.