I tried some of what you suggested and didn't really see an "improvement". I focused on the 502PIR, removed the engineer from the regiment and gave changed the formation to line. If you switch the force view to Op Plan, you'll see that once the regiment is formed up for the final assault, a company from each BN is task organized to form 3 separate groups, with A/1-502, B/1-502 and C/1-502 each leading one, and the rest of the companies interspersed. They seems unrealistic for regiment with no attached elements and completely organic. I would expect A,B,C to be part of one group, D,E,F in another, etc. Instead it seemed they got tasked out randomly to form the groups. You also don't see some of the desired behavior outline in the manual for complex attacks:
"If the attack is in line, often one subHQ will be tasked to exploit past the objective location; if there are three or more subHQs in the attack, then this will always happen."
The attack meets that criteria but it isn't happening.
I've attached two more saves. Example 3 is just after the attack launched. You can see the task organization for the regiment if you switch the structure to Current Op Plan. The attack goes in just fine, but it seems to me that it's lacking some realism and sense. In an attack like this it seems there is no reason for the battalions not to remain mostly organic, minus a few attachments here and there.
Have you checked the relative command strengths of all companies assigned to the attack?
If the companies selected to lead separate groups are those in the regiment with the highest command strength when compared to he remaining companies, it's conceivable they could be assigned field command leadership roles in the attack even if the units under their command aren't part of their original organic battalion formation and no battalion HQs are allowed to participate in leading the attack.