It’s called the “upper horn”, but I know what you mean 
On Fender basses (and many others) the upper strap button location roughly matches where the 12th fret is, and this gives the guitar a good balance point. I’ve never had any neck dive problem with any Fender bass.
I think it may be helpful to relocate the heel strap button on the SG. Moving it upwards a few inches should improve the balance slightly, but there’s a limit to where it could be placed due to the contours of the body. At least it would prevent the bass from rolling forward.
I’m surprised that Gibson hasn’t fixed this issue by this time . . . but, it’s only a minor problem and yes, I can live with it for now.
Ah yes, the tone . . . I’ve been experimenting with the knobs on the SG and it seems that if I turn the bass all the way up, the tone all the way down, and the treble 50-70%, I get better results. I almost sound like Jack Bruce now! 
Cheers, Joe
edit: I found that I also had to turn the master volume up on the amp a bit more.