Are those actual measurements of the box, or product dimensions from a manufacturer or vendor page?

Another thing to consider is your aircraft type(s). The 700s have larger bins; presumably the spec is based on the smallest bins? As long as the bin can accommodate the 10.25" height (keeping in mind you can't squish a box like you can a piece of soft-side luggage), you should be fine taking it on board. The other dimensions look to me to be considerably smaller than the average rollaboard, yet alone the massive bags folks manage to shove into the bins.

Also remember that you may be asked to sign a damage waiver indicating SWA is only liable for loss.

You could carry it aboard and use the gate check option as a fallback if you have trouble fitting it into the bin.