Adding air bags won't change your legal weight. That stays the same at 8800. It also won't change the axel or tire ratings. I don't THINK there is much difference to a F350 for that model year - maybe just springs. The 350 SRW were rated at 9900# GVWR and 20,000 GCVW.
Lots of people tow over limits with these and other trucks. The toughest challenge is facing a problem or emergency ahead. Will a 250 be able to steer away and brake at maximum force while maintaining control? I don't want to find out when someone comes out in front of me. As a parent I always picture a child running out or looking up at me through a side window as I helplessly try to avoid a collision.
Good luck with your decision. Exercise your good judgement.