To answer you question:
Sure you could use Corn Gluten now, unfortunately most of use have found it doesn't work very well as a pre-emergent. However it is an excellent fertilizer. The pre-emergent results vary greatly and for the cost, I think you will be disappointed.

With an organic approach your going to have some weeds, thats a fact. Now, there are some things you can do to limit the amount of weeds you have. Proper management practices that encourage a dense, thriving turf are the best method of weed control. Healthy turf shades the soil so sunlight can't reach weed seeds ready to germinate. A thick turf also minimizes the physical space available for weeds to become established. There are several management practices that will promote a healthy, dense grass.

Proper management begins with selection of the best turf species or variety for a particular area. For example, heavily shaded areas will support only a few turfgrass species. This results in thin, weak turf that is very susceptible to weed invasion. Do some homework before you overseed this fall and find the best variety of seed for your area and "shade situation".

Proper fertilization, watering and mowing are required to produce a dense turf that will prevent weed infestation. If turf is over-or under-watered, over-or under-fertilized, or mowed too low or too infrequently, the turf is weakened and cannot compete with weeds. Damaged areas resulting from using unsharpened mowers increase time needed for turf recovery, allowing for weed invasion. It is very important to understand that weeds don't create a void, they fill a void.

So, first,

Set your mower to its Highest setting and leave it there.

Always use a Sharp blade

Irrigate with 3/4" of water when 30-50% of the lawn shows signs of stress. In the shady areas you might be able to go weeks between waterings. The general rule of thumb is no more than once a week in the middle of summer. This is the most important step IMO.

To determine how long to run your sprinkler system to apply this much water, set out several straight-sided, same-size cans (tuna cans work best) at random in each irrigation zone and see how long it takes to fill them to the desired depth. Be sure to check your irrigation system for uniform coverage at the same time.

In the meantime get yourself a Weedhound(google it) or hand pull the weeds. You could also CAREFULLY spot spray the weeds with vinegar.

Thank you for the suggestions!

There is a 4 week window before and after putting corn gluten down where you should avoid seeding your lawn. Grass seeds need time to establish themselves before gluten is applied. The herbicidal effects of gluten will last for at least 4 weeks.

Unfortunately, scoot_cat is miss-informed on the herbicidal performance of corn gluten. It works very well, provided it is applied in the early spring and late fall before germination of the weed seeds occurs. The first year results will only produce moderate weed control, about 50-60% reduction. It is in year 2 and year 3 where the weed reduction will be most evident. You will see as much as 90 to 95% control of Crabgrass, Dandelions and broadleaf weeds.

Think about it this way. Your grass has been using synthetic STERIODS for a very long time, it will take a little while for the soil and grass to switch over to natural products. Chemical fertilizers give a large dose of rapidly released nitrogen for a quick green up. Corn gluten, on the other hand, releases it's nitrogen slowly over a period of weeks to months. The result is a healthier, more robust strand of grass.