Well I think you pretty much have two choices here and the choice you make depends on what you want.

If you follow the link to the site by Steve Hampton about the low tech planted tank, you will have noticed that he says you have to stay with a low fish load and have lots of algae cleanup fish. So if you want to do this, you'll have to do a cleanup of your tank to remove the algae and much of the waste from your fully stocked fish load (that will be feeding your algae), throw out any dead/sick plants, and add in a very large quantity of fast growing stem plants, as well as reduce your fish load and include a lot of algae eating fish.

If you prefer to stick with what you have now, a full fish load and plants that need to be nursed a bit back to health, you'll have to go the water change/EI method. I don't think there's any difference of opinion here, it's just two different methods for two different setups.

Low tech and non-co2 are not quite the same thing. A low-tech tank is non-co2, but usually what's implied is that it's low maintenance, meaning few water changes. These tanks required a low fish load and a very high plant load. Basically what you're doing is reducing the net waste produced over x amount of time to reduce the amount of water changes you have to do. Plants take in waste, and fewer fish obviously produce less waste. You're just stretching out your time factor.

Whereas a regular non-co2 tank can be fully stocked and you don't need it heavily planted if you don't want, it usually will be fertilized although not as frequently as a co2 tank, but weekly or every two weeks (in a well established tank) water changes are done to keep up with the amount of waste being produced by the full fish stocking. You're reducing your time factor between water changes, but you get to keep more fish and the health of the plants is easier to maintain since you can fertilize well and you are also removing the organic nitrogen that contributes to algae on a more regular basis. And the fish are usually healthier too.

I hope this helps clarify the options for you. If you want an approach that definitely works every time, the EI way does work, always. The other way is a bit more tricky because the additional organic nitrogen that builds up often leads to algae problems, and so much really rides on whether you have healthy plants in that system and due to the amount of variables, you may or may not have healthy plants. Either way you are not any more or less in balance, an aquarium is a man made idea and we pack in far more fish than you would ever see in nature in that amount of water even in a low stocked tank. We are maintaining an artificial system by doing water changes, the method you choose simply determines how often you have to do a water change to keep the fish alive in the artificial environment you've created for them.