I have not played TOAWIII, but I played ACoW and now I'm learning TOAWIV.
I'm not sure if my "techniques" will be helpful to you or not, but at least they might give you some ideas about how they might inspire your game.
I'll use FitE1 as my example (my game w/ GeneralJCL, me as the Soviets) ... we are around move #130, sometime in September 1942 and the Soviets are driving toward Pskov, while the Germans are driving on Sevastapol and Stalino to Stalingrad southern front. The Central Front is now in more or less "trench warfare" with very litle progress for either side, except that I have established some bridgeheads just west of Smolensk, and the city of Vitebsk is in my sights. So that's a current overview: complete AAR is in the AAR forums.
So, strategically, I already know what I want / need to do: keep attacking toward Pskov; keep trying to liberate Vitebsk; and reinforce the defenses in the South.
Here is where my "procedure" begins, with every turn: an "Engineering" check across the entire board, which will refresh my memory of map details, dictate what Engineers need to do (repair bridges, move to rivers for transport help where needed) and also help me identify any problem areas, disorganized units, initial attack planning, etc. --)
So, first engineering thing to do: DISEMBARK ALL "ENTRAINED" Units, using the "." period key, which locates the map onto an entrained unit. Press "." again on that unit, and it disembarks. Usually, I just use the drop down menu, "disembark entire stack" and if there is another in visual range, I disembark them, then it is "." again to locate any other entrained units. When pressing "." does not locate a train, I know all units are disembarked. Time spent: five minutes.
Now it is time for bridge building etc.
My technique for this stage of engineering is explained partly in the post #10 in this link
I don't have the FitE1 move in front of me at the moment, but when I get that, I will go into this step with more detail, because it is during this stage that I start planning combats, digging in disorganized units that I see, Etc., and then the "air check" phase, the "reinforcement" phase, and finally the "post-round 1 combat phase". I think TOAWIV has some tools for reports and map navigation that TOAWIII lacked, so some of my procedures might need to be "tweaked" for use in TOAWIII.
Anyway, great question! I hope I can give you some ideas later today.