simple trick that made installing my drain way easier

For a short run, I’d try adding small, even scoops of backfill on both sides of the pipe and alternating sides as I go. That seems like a low-fuss way to limit sideways movement without setting up extra braces, though the scrap-wood supports sound handy if the trench or pipe is especially prone to shifting.

Alternating small scoops sounds like it would help keep the pipe from shifting sideways. Do you also use it to hold the grade, or would you check that separately as you backfill?

Alternating small scoops can help limit sideways movement, but I wouldn’t treat that as holding the grade. The pipe could still rise or dip as the backfill goes in, so I’d check the grade separately as I go rather than assuming the balanced scoops preserve it.

What simple method would you use to check the grade as you add backfill?

A simple check is a level with a spacer at one end, sized for the intended fall over the level’s length. Lay it along a straightedge beside the pipe and adjust until the bubble is level; repeat at intervals as you add backfill. The required fall depends on the drain design, so use that specified slope to choose the spacer thickness.