Redution Of Child Support For Equal Parenting Time

I live in GA and back in 2004 my ex-wife and I agreed on an amount of around $500 a month in child support for 3 children because she made as much or more money as I did. I was writing and giving her checks in her hands every month. She got mad because I wasn't giving her the money in one lump sum, so she lied to the Child Support Enforcement Agency and told them that I wasn't giving her the payments as ordered. I went to the agency and proved to them that I had paid her and I was informed that she signed an affidavit saying that she was not to accept any more checks from me and that she was to inform me of this. The agency would not give me a copy of this document. In any case she didn't say anything.

Although I proved that she lied to them, they did not drop her case but continued to proceed with deducting the money from my check. Now it's review time and the state of GA. DHR is recommending that I pay $937.00 a month.

Although I didn't lose my job I have more expenses than I had with the first order which may cause me to foreclose on my home. My question is if we are actually concerned about the welfare of the children and time spent with parents, can the child support order be reduced or wiped out if I kept the children 1/2 the week and alternating weekends?