First of all, hats off to our first-time GM (of anything, ever) Stephen for doing a great job of the chaos!
Seems to me that one of the tricks with six players is managing the 'scale' of everyone's actions - I'll explain.
When it's just three players, it's easy to include most of the 'party' in actions. Somebody can lay down covering fire, another assaults. If someone helps either of those two, everybody's rolled dice, even if it's a very tactically simple situation (e.g. your squad vs. their squad).
When you have bigger parties, having the commando or section-8 make an assault roll for the whole shebang seems unsatisfying, so it seems you need to find a way to dole out the action.
Two routes occur to me:
1. Create tactically interesting engagements where the party is tempted to split up to pursue separate, supporting objectives. We had such a battle where we split into three groups to pincer a german squad car/roadblock/LMG setup that was nestled in some hedgerows.
Here, each group can be free to change their private sub-battlefield quite a bit with (say) Assault (and using naked 'Attack' very little), since a one-roll victory only carries the day for that sub-battle.
2. If you somehow skip this and wind up with an undifferentiated battlefield and/or mob of enemies, "zoom in" a bit.
We were in this situation when we stumbled through a hedge to find ourselves in an orchard, unexpectedly outnumbered by a surprised-looking German section eating at a field kitchen.
Several PCs' shooting actions might just be direct attacks against single enemies, saving the Assault for the explicit heroic attempt by the commando or section-8 to claim some ground, toss a grenade at the kitchen's parafin cannisters, etc.
It also occurs to me that it's sometimes worth polling a few players to see what they're doing to see how to parcel the action into moves.