Hi Joe, First off I am not familiar with this approach, I will google later. I typically use Manning's. I will say that a normal depth approach may be adequate. First I presume the normal depth approach shows that system is open channel and not surcharged. If yes, then the approach should consider the flow regime within the conduit. If the flow regime is subcritical then there could be back water impacts and the system could become surcharged and then operate as a full flow storm sewer. If supercritical, no losses transfer upstream an the one could use the direct step method to compute the flow profile through the pipe system. Hope this helps.

Open Channel Hydraulics by Richard French is a perfectly acceptable reference. however analyzing each section separately is prone to errors if tailwater conditions and other head losses in manholes and junctions are not properly accounted for. WSPG would certainly be a good software alternative to manual calculations for a storm drain of this size.