I am new to citrus and this forum, but I was a pesticide residue chemist for 25 years and although I try to avoid pesticides, I do use them when all else fails.
I read the link I found in the search and I have not yet tried the soap on miners, although I do use soap often on other insects. The problem is trying to kill the moth before the larvae start mining the leaf. Soap works by wetting the insect and causing it to drown, so you have to get the soapy water on the moth to prevent infestation. I will try it on existing infested leaves to see if it can get inside and kill the larvae.
I have used oil and it works with frequent application on any new growth. However, Millet told me on another forum that oil application at this time of year will reduce the plants ability to withstand cold weather, (you may live where cold is not a problem).
I have tried a pesticide called spinosad and it does seem to work. It is a relatively non-toxic pesticide to mammals (several thousand mg/kg if that means anything to you). It is toxic to bees, so try to avoid spraying flowering plants. According to the lable it can only be applied every 6 days and only 6 times per year, so target the primary flushes.