Yes, nominally 10x10, thus will be a Scott 581.
The important thing with this series is the use of a perforation gauge first
. Also remember that catalogs typically round the perf rate to the nearest half, so don't get too lost in the tenths. I took your image and rotated one copy to show that the top/bottom perfs are essentially the same rate
as the sides. It is NOT a count, but a rate, as I think you just figured out from rogdcam.
Secondly, don't get caught up in the very small differences in the image size between flat plate and rotary. There are better "first cut" ways when confronted by two similar stamps.
As a confirming trait, this particular New Orleans precancel was applied by the Bureau of Engraving and Printing to only certain issues. The only possibilities are Scot 581 (which you have) and Scott 632 (which is perf 11 x 10.5).