Catman,
Typically in our shop if we had to make plate girders we used the SAW process on a Bug-go and used a fillet weld at both sides of the web where the flanges are joined to web. On the side we started first we tilted the flanges out about an 1/8" or so and blocked it up in the middle if we did not what to add sweep to it. It was sort of trial and error like you are trying to get out of, but it didn't take but one ot two before you saw how much adjustment was needed. We ran passes on one side, turned it over and ran equal number of passes on the other side and never had "alot" of straightening to do. There was always some minor straightening and cambering to do. For that we used a blue tipped wrench and some hyd. rams to straighten the flanges.
Just curious, why you are making beams rather than buying them? W18's, W21's, and W24's are common beam sizes and are easy to find at any steel warehouse and full depth stiffeners or plating the flanges will really help if strength is an issue.
Maybe someone in the engineering field can post a calc. to help you in your problem of distortion from the heat input on one side. I'll keep a watch on this post because I'd like to know as well.
John Wright