I don't have an software suggestions, but it shouldn't take more than an afternoon to set up your own spreadsheet to calculate these factors, similar to the time it takes to familiarize yourself to new software.
The HL-93 live load is a combination of the lane load AND the design truck/tandem load at the position of greatest load. You must determine which has a greater load for that bridge, a design truck or a design tandem. For a simply supported span, see the following site for a tabulation of all...
Refer to the FHWA Steel Bridge Design Handbook Vol 13 "Bracing System Design". Staggered cross frames are discussed and refutes the DOT Reviewer on the fatigue cracks.
https://www.fhwa.dot.gov/bridge/steel/pubs/hif16002/
If this fails, you should ask for a source for his statement.
"Each face" means the outside part of the concrete, the perimeter (top, bottom, left, and right), NOT the middle core. The steel will be on the outer part of the beam.
Each direction means vertical and horizontal.
So on the top and bottom, the flexure steel controls, and on the sides the...
That example is lacking several figures to help visualize the problem. I took a look in the Seismic Design Criteria (where the equation is being pulled from) and it is also not very clear. [banghead]
The Concrete Pipe Association has resources on this.
The design manual: http://www.concretepipe.org/pipe-box-resources/design/design-manual/
There are a couple of examples, based on embankment/trench and soil type. There is also a design chart in the appendixx for embankments to save you the...