"Usually the only time we left face is a quick move on the field or guiding into a battalion line, don't do it too often. "
This is very common for reenactment units, and IMO it's a shame. Generally speaking any maneuver that can be done to the right can also be done to the left, and units should practice both ways. Too often we see battalions arriving on the field "the wrong way" and "countermarching" (actually two "by file lefts") the full length of their line. If they had marched by the left flank it would have been halt - front - dress - done.
"we try not to invert the company unless it's absolutely necessary."
Too many reenactor officers have never done a "real" inversion and think it means marching by the left flank. It actually means forming the battalion into line in "inverted" order - i.e. with the first company on the left.
Why would you need to do this? Well, suppose the battalion is in column of companies "right in front" (first company leading, as usual). It's easy to form line of battle to the left (the "proper" front) - you do a "left into line, wheel" and the companies are in their proper order. But suppose the enemy suddenly appears on the right flank and there's no time for any fancy stuff. Casey's Tactics describes how to perform the inversion:
By inversion to the right (or left) into line of battle.
484. When a column, right in front, shall be under the necessity of forming itself into line faced to the reverse flank, and the colonel shall wish to execute this formation by the shortest movement, he will command:
1. By inversion, right into line, wheel. 2. Battalion guide right.
485. At the first command, the lieutenant-colonel will place himself in front, and facing to the right guide of the leading subdivision: at the second command, he will rectify, as promptly as possible, the direction of the right guides of the column; the captain of the odd company, if there be one, and the column be by division, will promptly bring the right of his company on the direction, and at company distance from the division next in front;, the left guide of the leading subdivision will place himself on the direction of the right guides, and will be assured in his position by the lieutenant-colonel; which being executed, the colonel will command:
3. MARCH (or double quick—MARCH).
486. At this the right front-rank man of each subdivision will face to the right, rest his breast lightly against the left arm of his guide, and the battalion will form itself to the right into line of battle, according to the principles prescribed; which being executed, the colonel will command: Guides—POSTS.
487. If the column be with the left in front, it will form itself, by inversion, to the left into line, according to the same principles.