With regard to handgun ammo, is there an "ideal" 9mm AR barrel length?

I've been really drawn to the idea of SBR'ing my Olympic K9GL. I just kind of assumed I'd go 8", but now that I Look at it, 7" might be better.

I'm figuring 8" is roughly 91% the velocity of 16"
Figuring 7.5" is roughly 90% of the velocity of 16"
And figuring 7" is roughly 88% the velocity of 16"

I don't really have any idea what an inch of barrel weighs.

The point of the exercise is to move the balance rearward, reduce weight, and just generally make it a little more handy.

Mike