It’s a little hard to get your head around at first, it took me a try or two myself. Where you register zero does not matter at all (if using the two pin method). The pins are not along the edge, they are one centerline of your job. Either vertical or horizontal, does not matter, but you have to decide that when you create your new project and tell VCarve the material bounds and which way to flip. I did one using the edge method you’re describing, but unless you have an absolutely straight, square, same one all sides piece of material (not likely with wood) it will never be perfect. If you use the dowel pins you currently have to only square your material the first time, that’s ok, but the registration holes you drill into the wasteboard, then side 1 & 2 have to be centered on the flip. You do not re-zero X&Y on the flip, just Z, so where the original zero is irrelevant. Screenshots, maybe that will make better sense of my poor description:
Job setup: Note that I chose to flip top to bottom rather than left to right.
Centerline for flip: This is where that top to bottom flip happens.
Side 1: note 1/4" holes for dowel placement. Drill these into waste board, then center your material as good as possible to this and drill same holes into material using this same drilling tool path. Flip material again, using pins for alignment, then drill same hole toolpath on opposite side (be careful not to go so deep you hit the dowel pins). Also note Zero X & Y, this is where you initially zero your machine.
Side 2: The material is now flipped, but machine zero x & Y stays the same (You can barely see where I put the “zero X & Y” text on the opposite side, it’s now at the top left corner, but machine zero stays the same (darker text bottom left corner)
Preview: In this preview I made the same profile 1/2 of the way through the stock on each side. Obviously it needs tabs and such, but this was my 2 minute example.
Hopefully that makes sense. Try some small scrap with a simple design first maybe?