I think I would brace all of the legs before starting on the top. You don't need long braces tying all of the legs to each other, just some short 1 foot long 1 x2 lumber tying the legs to the frame for triangulation would serve the purpose of strengthening the benchwork tremendously.
Thanks Russ. Shortly after posting that update that very thought occured to me. It would not make sense to do it any other way, especially in my quest to keep construction costs as low as possible.