Hi C.,
My son also had eczema, starting at about 12 months. We treated it at first before doing diet modification, and what worked best were products with no SLS or SLES, or preservatives. I switched exclusively to California Baby super sensitive hair and body wash (available at Target and Publix, but you can get it cheaper and in bulk online). It may seem a little pricey, but a little goes a long way, and it lasts a long time. even products like Johnson's and Aveeno have SLS or SLES in them which is known to aggravate eczema. And for lotion, I found Baby's Bliss DermaCream. It is available online, and it is the only thing that seemed to work to calm his skin.
Both these products seemed to help immensely, but ultimately, the only thing that "cured" his eczema was eliminating the things he was allergic to from his diet. With him it was milk and eggs. It was just trial and error on our part,as we never had any formal allergy testing done. I waited until he was two, as I did not want to take him off milk before that. Once he was off milk and eggs for three weeks, his eczema was completely gone. Also, I know that SOY can actually be a highly allergenic food, so that may be why you did not see a difference when you switched. Also, if he was still eating other foods he is allergic to, that could do it.
I would do a test run, and try eliminating all the things you have noticed him have a reaction to, for one month and see if you notice a difference with the eczema.
My son has been off milk and eggs for about three months now, and I let him eat scrambled eggs for breakfast last Sunday, thinking, "oh, one egg won't hurt." Well, by Monday evening he had eczema patches on his legs and elbows. Now I know, yes, just one egg will do it.