Has anyone lengthed an existing bridge?

Has anyone lengthened an existing steel bridge? Google wasn’t any help. Here’s my dilemma:

I’m working on a design-build tender. The project involves a number of bridge replacements and bridge retrofits. On the retrofit bridges, the owner wants to lengthen the existing W33 stringers and keep the deck. And they don’t want any sag and they don’t want a rigid frame.

In the image below, the as-built bridge is cambered 3/4" to level out. One problem is trying to predict the deflection. The two professors (yes they are) who have been studying it this week don’t really understand the problem. At first they’re telling me the new deflection is 1 1/2", but it turned out that value is for the W33 with a completely new deck; although the net deflection would be about 3/4" (1.5" - original camber). Then they came up with a stiffened girder to hold the deflection to 3/4". To me that probably doesn’t work because the girder has leveled out.

Yesterday I came up with a crazy scheme to minimize the girder sag. I add the 15’ of lengthening at each end but leave it as a cantilever when the deck extension is cast. I calculated that produces an upward deflection of 1/2" (original DL camber is about 3/4"); after the bearings are installed and the temporary supports are released the deflection, assuming the composite section, is a little over 0.6", leaving a 1/8" sag. As a precaution I could stiffen the bridge with side plates at the bottom of the web and reduce the deflection to about 1/2". In theory - or more like in my mind - it balances out.

The bridge has vertical curve camber, (max. of 6")so no one will see the dead load sag but it was built with 14’-6" vertical clearance, which can’t be reduced. I should be able to jack the superstructure an inch or two as long as I don’t violate the vertical requirements for the bridge above. Any thoughts would be appreciated, thanks.