I would avoid like the plague the idea of being staggered at taking more damage than my CON score, especially if that number is close to 10 and fighting a barbarian or fighter who got a lucky hit.
What about baseing it on the Massive Damage threshold then? Take half that number. So, any damage of 25+ points would stagger the target unless the Fort save is made.
Even if you did go with the CON score, you could throw in the save so that higher level characters are less likely to be staggered.
You're right about the 10 CON, though. Half the Massive damage threshold is probably a better idea, easy to remember, and the character can still resist with the Fort save.
Maybe make the Fort save a 10+ throw instead of 15+?
If the Fort save is failed, then the character is staggered for a number of rounds that the save missed by.
For example: Fred the Fighter takes 27 points of damage in one blow. This is over 25 points and has the potential to stagger him.
He throws a DC 10 Fort Save and rolls a 7. This means he will be staggered for 3 rounds.
Just thinking out-loud here.
Something like this would be a hoot when taking on the Fire Giants, huh?