From an Organic viewpoint, don't poison the land. Weeds and other undesirables are Natures way of trying to protect the soil from erosion. They thrive in poor soil conditions. 'Top Soil' labeled....same thing. Poor soil full of unwanted seeds.
Improve the soil and the weeds will give up.
Clay over sand, very little (if any) nutritional value. Not much different than a track builder spreading a few inches of sandy loam over rock, laying sod, watering the heck out it and then moving on.
Not much there to eat, so to speak. Very little (if any) microbial action going on.
I'd be looking towards something more compost related for a growing medium. We have something available in this area that's relatively inexpensive ($30/yd) called Tx Hardwood Mulch.
Not a decorative bark mulch, it's more of a rich fully composted mix. It's what I use in all my raised garden areas and dead or low spots in the turf, as well as a seasonal lawn dressing.
Followed with regular feedings using a seaweed based lawn supplement, something like
HastaGro 12-4-8 Lawn Food
Long term plan, this ^ stimulates deeper root growth, opens up the natural soil aeration and adds beneficial microbes to the mix.
You'll water less and have a greener lawn than the neighbors, thru extended dry conditions. And the weeds won't have a chance.