Any lawncare is going to be tuff right now. I believe I have seen you make this post in the past.
Good weed control includes several things, when not utilizing weed killers (non-organic)...
*You need a good watering regime, one which promotes a healthy perennial grass lawn, as opposed to helping germinate weeds. Once you have grass established, this is simply deep watering, no more frequent than necessary.
*You gotta keep a thick lush lawn, that means optimal fertilization, and proper mowing.
If you can ever get a thick sod (from seed), then you will be set. In bermuda grass pastures (i.e. coastal, one of the best ways to out-compete the weeds is applying a high dose of nitrogen) doing so gives the bermudagrass and edge, as it's amount of growth is very dependent on fertility.
Bermudagrass seed is fairly cheap in reality, so I would keep throwing on more in bare areas, during a normal yr. This however is not a normal yr... and I would personally wait at least till we get some fall rains, to do much of anything.
For now, I would focus on things like adding organic matter (i.e. manure compost to your lawn) rather than spending money on corn gluten meal and molasses. Honestly, corn gluten meal is very expensive, and not very effective, unless you apply very frequently... which ultimately makes it cost prohibitive, and not worth the money.
If you really want to utilize molasses, I would focus on utilizing liquid molasses... If you can locate feed molasses for say $5 dollars per gallon or less, then you have a good deal. The horticultural grade molasses goes in the $10 dollar range.
Manure compost will add most of the nutrients your lawn needs, while also building up orgnaic matter in that dry sandy soil that you mention.
Also, for weed control, both of your two main enemies are burrs... So, get out some old carpet and drag it across your lawn... this will pick up a lot of the burs out of the dirt, then simply discard the carpet. Repeat this process after each season of burr production.
Lastly, when you do finally have some good bermuda, start mowing HIGHER. The taller the grass is, the less sunlight that hits the ground surface, and therefore, the less weed seeds you have germinate.