Moving the origin doesn’t change what’s sent to the laser, it flips things in the workspace. If you change the origin, you should see your shapes move around within the view, and flip. Select them and press H to flip horizontally, V to flip vertically. When the design you see matches the design on the laser, you’ve got it right.
There’s an easier way - Click this button:
Then click the Red square in the corner of the page:
Whichever corner your laser moves to when you do that is the point you have to choose for your origin.