Your sanitary conditions are probably why most Asians almost always cook their vegetables and do not traditionally eat it raw.
If your ground water is polluted, in all likelihood the beaches if frequented by a lot of traffic and if your polluted streams empty nearby they may also be polluted.
Cow manure needs to be composted or aged first otherwise, same problem, the e. coli and other pathogens in the manures may make its way onto the food as well. Manures need to be aged a minimum of 120 days. No fresh manure can be piled on top of an old pile or start the count again.
Sterilizing soil is possible but it really stinks and unless you have a soil sterilizer, it would be hard to do it in quantity.
If you can get commercial potting soil that would be the best thing in pots.
Peat moss and coir are sold in bulk. It is usually mixed 50/50 with something that provides drainage like perlite, sand (clean coarse sand, not fine sand) or cinder. Perlite is the lightest, cinder provides good drainage but it would be hard to grow root crops in it. You can add compost to the mix up to about 20%, but it is hard to put manure in pots without being very careful. You can used fish emulsion or slow release fertilizer. You would have to check around for an agricultural supplier or garden shop.
If you grow vegetables that do not touch the soil and you can test your soil for pollutants it might be worthwhile to plant in ground with aged manure and make your own compost. Beans, squash , cucumbers, tomatoes, bananas, and things that you can trellis to keep of the ground may be better than root crops. If your back yard is not near a factory, septic system, or highly traffic area like roads, there may not be that many heavy metals in it. The heavy metals are more important to sample than the other pathogens as they will accumulate in the body. If you site your garden on high ground, and you test the soil, you may be o.k., as long as you don't add anything that would contaminate it like fresh manures or contaminated water from a pasture. You would still need to wash the veggies and preferably cook them well to kill pathogens.
Phyto remediation is being used to remove toxins from the soil. It is an efficient way to remove known toxins especially heavy metals. It requires testing and selecting the right plants. The plants are pulled and discarded and not eaten but after they have cleaned the soil, (you would have to retest to see if levels have been reduced enough), it should be safe as long as it is not contaminated again.
https://www.resilience.org/stories/2014- ... nated-soil
You have a huge back yard. I am envious.
Happy gardening in Hawaii. Gardens are where people grow.