Thickness can work both ways (help and hurt).
I find thickness more important for cuts than other items, so I can agree to a point.
As to positioning, using a 12x20 design page works great (even if the camera looks like it is not)
The thread below was an experiment just to see actual differences using variable focus on an engraving. I was curious if the wide splash on an unfocused score would look that much different than an engrave.
It did not look that different, but I was blown away with the time differences for the design.
If you have a Large item, or lot of something (like shown) to make, time wise it would be a benefit to play with the design and try a large de-focus score instead of an engrave.