audwilly, I am hoping for your sake you had these tji's engineered. This way you can let the problem be a pain in his back. If not, call the manufacture and find out from them the recommendations to beef up there product. I recommend in this world we live in today to do a lot of CYA.
I sympathize with you on a issue like this. 22 years ago we were working a job were there was a lot more deflection on a floor than we were comfortable with also. I do not know what the deflection was, it was just to long ago. What I do remember is we had used 2x12's on 16" centers. I also remember inserting 2 more 2x12's between the floor joist and jacking the joist up in the center, tilting the new 2x12's up, beating then in to place and lowing the jacks. When I looked up afterwards and saw all those joist on about 5 1/2" centers I could not help but laugh. We then were able to go to the second floor and nail the decking down to the new joist. What a pain this was, even for the electricians.
It is a different world in construction today than it was 20 or 25 years ago. It just seems people are looking for a why or excuse to get something done a not pay for it.