Thankfully, I was able to laugh at our opponent's ingenuity (it's only a game, after all). Funny enough, I 'rationalised' it with the old 'smoke on the battlefield' ploy myself (taking care not to mention mirrors).
Incidentally, the Croats didn't actually enfilade the leading Grenadier battalion; they had skipped past that one, rushed into the rear area (my Scooby Do moment) and instead, enfiladed the following one which was marching up in support! That Grenadier battalion was able to turn to face on the next turn but the Croats then simply skipped to the side again (i.e., further into my rear) before the firing phase (only then did I remember Crossing fire - hope we got that one right). After that, the Croats ran amok behind my lines (pursued by the 2nd Grenadier battalion) including routing an artillery battery and temporarily capturing the guns (which were then recaptured by the pursuing Grenadiers)! Rather ominously, our opponent is talking about painting up two more Croat units. The one he has is quite well painted - I must check again however - did they have an "S" painted on their chests?
This double move business in the proximity of the enemy clearly needs greater respect!
It might not have stung so much if it had been in woods, but it was in open terrain, mainly! As it happens, it had little effect on the battle, as Westmarcher ably and handily routed the Austrian and Russian grenadiers and opened up the enemy flank. I was commanding the other half of the army, which was less successful! For the record, it was a post 1760 game. I think the solution would be to apply the crossing fire rule.