Organic herbicides are either based on fermented plant acids or essential oils. None are particularly effective.

Studies show around a 40% overall effectiveness that increase to about 60-80% provided the weeds are young enough (cotyledon or first true leaf stage ) and the concentrations of the herbicide high enough. Plus one needs to factor in air temperature and amount of sunlight as well. Broadleaf weeds respond much better than do monocots or grass-type weeds.

IMO, you are not going to get a very satisfactory kill rate on turf grass with an "organic" herbicide. If you can find the horticultural vinegar (20% or higher acetic acid - not diluted) you may have some success but will need multiple applications. If you want immediate results, use a sod cutter to lift and remove the sod, which you can store upside down to compost or simply add to an active pile. If you are willing to wait a season, do the cardboard/newspaper topped with compost smothering route.

Most all "organic weed" killers use acid (Acetic Acid or Vinegar), fatty acids (soaps), or essential oils in an attempt to control that unwanted plant growth. None are as effective as simply denying those plants of access to sunlight by using mulches.
Vinegar, purchased in the grocers, will be about 3 to 5 percent Acetic Acid, already quite dilute and it will not be very effective. Sometimes Vinegar for "weed" control can be found in garden shops and at 10 to 25 percent Acetic Acid they can easily cause burns on you so due care in handling is necessary.
I would just till the area and put what is growing there right back into the soil and not concern myself with a "weed" killer.

We're going to till a new 50 x 50' garden now in lawn grass and keep rows tilled during the season to reduce weeds.

Closely mow the area, spread a layer of unwaxed cardboard, then top it with mulch and compost and clean dirt.

A thick layer of wood chips in the paths should suppress the grass, unless you have Bermuda

Agricultural vinegar has to be applied full strength, with appropriate protective gear, onto seedlings and young plants.

None of the recipes you see on Pinterest (vinegar and Dawn detergent and salt) work worth a darn, and I don't want to mess with agricultural strength acetic acid. Which is why I use generic glyphosate when I want to kill plants: it's cheap, biodegradeable and effective.

Here's the MSDS for 20% acetic acid - the "agricultural vinegar".
http://www.setonresourcecenter.com/msdshazcom/htdocs/MSDS/E/EMD/Docs/wcd00036/wcd036fd.pdf

Here is a link that might be useful: Vinegar VS glyphosate

" I use generic glyphosate"
Which says that person is not an organic grower.

If you are going to be tilling between the rows regularly do you need a herbicide at all? Cultivation, such as hoeing, is an effective way of keeping on top of weeds between crops and you can't use a herbicide amongst crops.

I'm not dogmatic about any gardening practice. My usual reaction is "do nothing except maintain optimal water and see what is really needed".

I practice "IPM" ... I use whatever will have the least impact and still get the job done in a reasonable length of time. If the garden sprouts a nest of fire ants, I'm opening the Amdro, not messing around with home remedies. The wasp nest in my tool shed, OTOH, will get the soapy water treatment tonight. She's right on the handle of my pole saw!

http://www.epa.gov/opp00001/factsheets/ipm.htm
http://www.ipm.ucdavis.edu/GENERAL/whatisipm.html

For weeds, it may mean a scuffle hoe or hand-pulling, it may mean one application of glyphosate (better than multiple doses of AvengerAG or SummerSet AllDown because it kills the roots of perennials like Bermudagrass).

http://www.summersetproducts.com/assets/AllDown_Concentrate_label.pdf
http://www.summersetproducts.com/assets/AllDown_Concentrate_msds.pdf
http://www.avengerorganics.com/LinkClick.aspx?fileticket=A4SpfYmxDWQ%3d&tabid=81

We tried corn gluten meal as a pre-emergent. The quail loved it. So did the doves.

The two main purchased additives I use are soil sulfur and Ironite ... because this is alkaline desert dirt. The compost and mulch is all home-grown.

If not too late in your area, till it, then 2 weeks later till again. the 2nd gets the stuff that regrew. If you put weed cloth in the rows and a layer mulch or even a then layer of dirt on top of it you won't have to till, I put weed cloth where I put out vines. As long as you buy the heavy duty you can take it up in the fall or next spring and rearrange each year.

but to your specific question. I don't know anything about it