I've worked for a pest control company in the past and the best information I can give you is to make sure you don't have any branches or foliage touching your house, and make sure there's no standing water around a 10 foot perimeter of your home.
If you've covered every hole you can imagine (which is next to impossible since ants can crawl through holes we can barely see) then those are your best options.
As far as I know, there isn't a non chemical way to effectively remove a colony of ants. A few always get away. Now, are you aware of what type of species ants your dealing with? It's important. Some ants have one parent mound while others have a parent mound and the colony will build "satellite" mounds all over the yard. The satellite mounds will be smaller, but any eradication won't be effective without removing these mounds as well.
If you decide your fed up with ants, and you're ready to try chemicals, I have three products to recommend that are safe, and very very effective.
1) Temprid SC
This product is made by the bayer corp. This product eliminates over 50 species of common household pests. This product will leave a residual film of product for up to 30 days on the outside of your home. Also, for mosquito control, you can spray plants safely with this product and the mosquito population will almost vanish around your home.
This product was our base product and we've had very positive feedback from our customers homes we've treated.
2) Termidor
This product is made specifically for ants and termites. This product effectively removes ant colonies for up to 6 months. The ants will track through the residual film of product and live to carry it back to the colony. The other ants will get this product on them as well and the whole colony is thus eradicated. Very effective. We were only allowed to use this product twice a year, but nothing could beat it when it came to ant control.
3) Phantom.
Just as effective as Termidor, but you will have to apply this product every 30 days to the outside of your home. It kills the colony in the same fashion as Termidor as well. It comes in an ultra concentrated liquid, and an aerosol form as well (good for indoor treatments).
The company I worked for had very positive feedback for all of these products. The company I worked for was a very reputable company as well. It's presence reached 5 states and is still expanding to this day.
That's the best information I can give you. These products are very effective, but are useless without a good pest management program consisting of home cleanliness and hygiene. You have that covered, so the choice is yours!
If you decide to continue with a non chemical approach, I respect that and would like to know what method worked.
Thanks for reading this long winded post!
Joe