DL, I've daydreamed about a modified wheelbarrow (with an iron wheel, of course) with a flat bed that's level when at rest that I could then fit with custom made boxes (several so none are too heavy) that sit on and lock into place with the tools divided as you outlined more or less. Complete with waxed canvas cloth that snaps on.

But alas, it remains a daydream and for now I use an open top tote that's maybe 12x20x5 that I fill with the tools for the day. When I go to site I take a long tool bag that holds my hand tools -- more general carpentry stuff with a chisel and mallet thrown in.

I have also gotten where I try to do more with fewer tools to lighten the load. One chisel, one mallet, one saw, one axe, one knife, one slick, one plane, and a framing square, 1 foot rule, awl, chalk line, and pencil and I can just about build anything. (doesn't count the drill and mortiser)