First instinct is start your mixes with your master fader backed off a few db.
Also, do you have absolutely nothing on your 2-buss? Nothing outboard between console and converters? It's fairly standard these days to touch your 2-buss with a little light compression for glue or a touch of eq for overall vibe. I'm not talking about stepping on the Mastering Engineers territory...nor am I telling you that this step is necessary. I was just asking. So, if you are comfortable, and have no desire for additional processing before your A/D, Master Fader is your answer! Many of us rely on the Master Fader from time to time for some level taming.
I run my mix through various things pre converter. One move is a pair of vintage 1073's line in and have fader trim outputs to help balance your L/R...if needed. This is a nice mojo move. There are tons of "Neve type" amps these days if you want some extra voodoo with level control. Or pick any other wonderful flavors of line amps, super clean to super signature sounding. Just a thought.
I hit my SSL pretty good. My output meters aren't pegged, but they are pretty hot. That's where a good rock mix comes alive on an old SSL.
Good luck!
JJ