Well I'm guessing that "Proprietary Component A" listed in the MSDS is the wetting agent. Not knowing what that is can be worrisome. The fact that is claims to be organic is ok, but doesn't cinch the deal of making it safe. But it does seem to address your primary concern.
I don't know how much the stuff costs, but judging by the ingredients (for the granular), it looks like you could replicate it with some baby
shampoo (wetting agent), ironite (or similar iron-based greening agent), and
chicken poo. It's cheating though to say that the reason for the perk up is because of better water penetration given this formulation. True, water will make it stand tall and feel good (maybe greener), but iron and nitrogen given at the same time sure does that too! If you're happy with your fertilizing regimen, then you could get by with just the baby
shampoo.
Wetting agents (IMHO) can possibly speed up soil busting/aerating on the theory of improved
root vigor. But you have to keep using them (as an added step) while that process (still running at the speed of nature, or slightly faster) executes. Not a horrid prospect if you are so motivated and have the time for the extra step and the money to keep it going. I've been tempted myself. Then I decided that the extra effort and expense for the amount of dirt to treat wasn't worth it to me.
If you keep up the mowing high and try to water slowly (like it sounds like you are: watering until just before runoff, resting, then watering again, perhaps even repeating until you get 1" in one watering) then I think you'd get the same results, since the water will penetrate eventually.
Dandelions are doing you the service of busting soil with their long taproots, so you have a negative becoming a positive, or at least a net neutral.
If you keep up the mow high and water deep (and keeping the chemicals off), worms will find your yard again and help even more with the soil busting and root penetration (and fertilization!). Nature can heal it!
If you feel like joining the experiment, you can try digging some worm pits. Search around and find Northeast Al (now Al Loria) on this forum to hear about his trial of worm pits. So far a positive, from what I read!
If you want to watch your
land rally, just keep up the mow & water mantra, it's a sight to behold when your lawn takes that turn for the better! You'll get more topsoil every time you mow high and leave the clippings, or every time a worm poops in your soil, or a weed dies, or grass dies, or anything else breaks down on your lawn. Adding the soil/compost in the fall ought to help (if you know the make-up of the delivery is better than what you already have!), but sure is a lot of work and expense to start from scratch again.
A soil test would be great, to find out what you're lacking as far the soil environment for the grass.
Whew! Didn't mean to write so much!