It may be too late for this or it may have been addressed in another manner. To my eyes, the lateral bracing seems absent. I did see the suggestion to add 2 x 4's for connections between the legs in conjunction with "L" brackets, but all too often, it is so very easy to allow 2 x X construction to get slightly out of plumb or square. Plywood is an another ideal solution as long as two "factory edges" are attached to outside planes.
What I mean is that I would not trust the surrounding elements to correct the side-to-side or front-to-back tendencies an out-of-plumb (or -square or -level) stand might have.
I would use screws to assemble the stand, for the additional piece of mind. It is a bit hard to tell from the diagrams and descriptions but I am guessing that the "notched to fit" means that a 1.5" section of the 4 x 6 will be removed, allowing the 2 x 6 to rest on the four corner legs. This seems very reasonable but I would go a step further and remove 2" from the 4 x 6 on both sides, allowing me room to "face" the 2 x 4 with .5" plywood, glued and screwed. That plywood could be cut to run down the 4 x 6 and then s&g'd to the 4 x 6 (6 - 12" past the bottom of the 2 x 6, necessitating removing .5" from the faces of the leg to allow a flush fit). The plywood is then incorporated into the stand without changing your proposed cut lengths.
Lastly, it appears from the diagram that the two 2 x 6's in the center are face-mounted to the 4 x 6's. It will be stronger to cut your two center legs down by 5.5" and make a header out of those two 2 x 6's. That allows the leg to carry the weight and not the item you use to attach the 2 x 6 to the leg.
I hope that helped but I fear it may have confused. If any of my response is unclear, I am happy to clarify. And I apologize for offering advice on a design that I may have mis-interpreted.
Best of luck with your build! Tagging along....