Ask the player to play 8-th notes with good attack and watch the tuner. It should give you the same numbers your guitars gave (0 strict, around +5 cents, etc).
Then depending on sections, retune the bass. When he plays really fast 16-ths with less attack, he'll tune differently.
When he hits the long notes, he'll go flat in the end. I teach the bass players to watch the tuner and press the string more on the fret in such cases. Pulling the neck backwards works with open strings.
Being the bass player myself, I tend to play without too much strength. There are many ways to achieve a focused and agressive sound without punishing the strings.