A.F.
My daughter has the same problem - not eczema, but SUPER sensitive skin that keeps us constantly fighting diaper rash.
We were controlling it well for a long time by cleaning with soapy wipes (I cut up microfiber cloths and keep them in a solution of bath soap and water - or I keep a bottle with the solution in it and spray it on her and then dry her off). The ONLY thing that will remove fungus and bacteria from skin in the diaper area is SOAP.
So, my suggestions are: don't use commercial wipes during a rash - if you do, rinse them out first to prevent the chemicals from further irrritating the skin. After all the solids are off, wash with soapy solution (either homemade wipes or rinse with spray bottle), and DRY really well.
Over-the-counter anti-fungal (athlete's foot cream - works as well as prescription most of the time - you can get a 4oz tube at walmart for $5), and then a barrier cream on top.
My daughter is now 20 months old and the rashes are getting more persistent. The doctor added a compounded prescription that is a "bile binder" that should help keep the acidic/irritating components of the BM off of her skin. When her BMs are a little less solid, I use that and it really does help.
I found this online: "For stubborn cases of contact diaper rash, a prescription cholestyramine ointment works by binding up the bile acids and pulling them away from the skin." (http://www.metrofamilymagazine.com/July-2011/Diaper-Rash-...)
My daughter's skin will turn bright red from nearly ANY contact with BM.
I used to use a barrier cream called Calmospetine and it did a good job, but I saw that another cream called Pinxav (pronounced "pink salve") was highly recommended by moms who used it and I really like that one, too. Seems to be doing a good job on her sensitive skin. Has a somewhat strong pepperminty-smell.
So - to sum up, make sure you're cleaning with SOAP after each BM; don't further irritate already rashy skin with chemical, commercial wipes; use an antifungal and a barrier cream (really slather it on); and if all else fails, ask your doctor about the bile binder prescription.
Good luck! I know how much it hurts to see your little one in pain when you're doing all you know how to!
Added: Oh! And during a bad rash, put some baking soda in his bathwater.