The weeds are trying to tell you something.
Ok, so first, I am an engineer by trade am not a farmer, however I have lived on a farm most of my life and both my brother and father are farmers. They would be quick to tell you that the weeds are trying to tell you something. We would have what is arguably the best grass airfield in the state and it has no irrigation nor do we use any herbicides or insecticides. Most grasses that we try to grow on airfields are relatively short rooted and need high nutrient levels near the surface. Many of these weeds you talk about have much deeper tap roots that are able to reach deep into the soil. They in turn will bring nutrients to the surface, which once mowed/slashed will decompose on the surface and become available to the grass, and eventually the grass will take over. If you spray these "weeds" you will stop them from performing this benifinial lifting work. To accelerate this grass domination process you can add an NPK fertilizer, correct your pH, or add a trace element of necessary, however if you are going to go down this path, I would strongly recommend you do a leaf or soil test to determine what is lacking, otherwise you are just throwing away good money that will either leach into the sub soil or break down and disappear into the atmosphere. Most farm stores near you will be able to provide this service or put you in contact with someone that can, as this is a very common practice these days. Testing is generally far cheaper than blindly throwing fertilizer at a problem.
Back to the mowing/slashing side of things, try to keep your grass on the longer side of the tolerable range if you can before you cut it, but not so long that the mowing swaths leave mulch so heavy that it kills what is beneath it. If you cut things down to the boards regularly, them there will be little root mass beneath the surface. This root mass is the plants inertia that helps it ride through dry and west times without dying off. Generally a mower or slasher that chops the grass up well and distributes it evenly will be more benifinial than one that lays it down in heavy narrow swaths.
Regarding the use of 2,4-D and other such compounds, using these in a situation to try and fix a pasture/lawn problem is like taking antibiotics or antiviral tables to correct an illness when you are living on a diet of fast food and soda. If you correct the diet, the illness will generally take care of itself, it's just that for the last 50 years chemical manufacturers have ingrained in us that we need to be spending he money on killing what we don't want when all we had to do was focus on encouraging the plants that we do want to grow.
For more information on this approach a farmer by the name of Peter Andrews has written two books on this topic ("Back from the brink" and "Beyond the brink") and even for an engineer they are a riveting read. They will completely change the way you look at farmland and the landscape in general.
It is encouraging that you are thinking about your groundwater. As someone who has previously operated as a crop duster loader and applied more gallons of chemicals in an hour than most people will see in a lifetime and seeing the birth defects and other problems caused by these chemicals, we have a saying that if it kills sh-t, it kills you. Every one of the chemicals or compounds now banned for general use (asbestos, many organophosphates etc.) were once defined by the governments(s) as "safe", so I treat anything that is designed to kill other organisms (plant or animal) with utmost caution. 2,4-D especially so, as its one half of Agent Orange.
I hope this is of some help and if you want further assistance with diagnosing the root cause of you lack of grass dominance, PM me and I can put you in touch with some pasture specialists who can assist you further.
Cheers.
Tom.
