I'd run a Regt as three separate entities (combat Bn (possibly a task-force, but most frequently the organic formation), combat Bn, HQ-Support-Reserve. This latter broken down and recombined as needed to move elements within the rear area. My supply network is often 'commanded' by some rear area HQ with 'defend in place' orders - individual depots moved and then re-attached to the LOC HQ - with smaller scenarios and no strong pressure on the Map Boss I might not combine them into one formation tree, but rather leave each as a fourth semi-permanent entity within the Regt.
For Admin moves, and for resting units I will reattach all Regt assets to the Rgt HQ (and maybe all Rgts to Div HQ) to minimise command load, but I don't find a particular problem in disposing the Bn in a tactical manner - where this exceeds the level of command authority actually exercised by a higher echelon commander, there is a higher level of implicit command given with phase lines, boundaries and orientations than is easy to accomplish for complex attacks.
There is also far more scope for timings to go off with the separate elements, and this opens opportunities for commitment of reserves, or for attacks to get fundamentally bogged down, which requires player intervention to identify, decide, plan and act.
Within the Bn, where a lead company is being engaged effectively I will permit it to deploy and SupportByFire (SBF) the continuing movement of it's parent formation. This is similar to running the Bn on aggressive settings, but I find that this bogs the whole formation... using medium or low aggro keeps movement going, and the SBF protects the moving elements. It also allows a longer period of artillery suppression of enemy positions in the interval between detecting a definite target and being too close for support. There is less risk of a SBF formation being effectively engaged than one that is moving at closer range, and therefore a lower risk of retreat or routing... if the unit is forced to give ground, being further away will usually permit a cleaner break from contact and fewer casualties to fire and surrender.
Where I am operating two units 'together' then I will use one as the HQ for the pair, or designate a formal HQ unit to control them. Where elements are operating as fire support for, or as the reserve of the Parent unit (often the same unit in the mid portion of the assault), then they will usually be 'singles' until recombined for further operations. These might be to regroup 'on' the objective as the formation reorganises following success, or to join with other reserve elements to advance and block enemy movements or to pursue routed enemy elements.
What I will avoid is reattaching companies or platoons to an HQ which is actively engaging in mobile offensive action. The last thing you want is a long reorganisation or replanning while in contact. I would rather form a parallel ad-hoc grouping from all the detachments to act as my fire-brigade and then try to bring them into contact with a major formation which they can rejoin smoothly (at the beginning of a new orders cycle is a good time).
While some of this might sound chaotic, I am actually more strict with movement routeing, echeloning and unit boundaries than the AI tends to be. I avoid attacking 'across' other unit's areas of responsibility and try to keep units sharing a supply source together geographically, with the supply feeding from the units' rear. I also attempt to maintain a coherent front... and where that isn't feasible to at least screen the road network between major combat formations.
That this won't always work out should of course be assumed, but the effort is there, and frequently makes the difference between a resilient and tough force, and one that is easily brushed aside.
Is there a chance that you might upload a screen shot from in-game where you have units positioned according to your second-to-last paragraph. Sometimes, okay often, I have trouble visualizing your descriptions. I often try to draw out what you describe and see if I can follow all of the points, but sometimes a picture would help immensely.
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