I guess I'm the rare exception here. When CPS in Montana seized my great-niece, I was asked by my niece to fight for custody. It took less than 8 weeks to satisfy the assigned caseworkers in two states as to our fitness and determination, and we visited the baby every other week (2,000 mile round-trip) during the waiting period. The ICPC arrangement qualified us for many benefits in our state (WA) including developmental assessments and treatment as needed.
We had a caseworker who visited at least once a month. She also helped us navigate the system and secure benefits like Medicaid, dental and nutritional services, and the TANF grant ($364 a month in our state -- it varies). Although this is Aid to Needy Families, it does not require
you to be needy. It considers the child as needy and is based on the child's financial circumstances, not your's.
When my niece and her husband were TPR'd by trial, both state's offered to help with our adoption paperwork, but we opted to adopt privately using the attorney we had originally hired to be the child's Guardian ad Litum. Had we used our state's social services, our daughter would have qualified for continuing benefits including a free college education. It was our choice to adopt privately because we hoped to avoid some of the stigma of a CPS adoption.
We had our daughter with us for six months under the Kinship Care agreement, which is really little more than a contract to babysit for the agency that retains custody. You must have their permission for everything from childcare arrangements to travel plans. We chose not to apply for a foster parent license because of the extensive training required and the backlog of people waiting for the classes.
We were given permanent legal custody by the trial judge on the day the birthparent's TPRs were finalized. Our petition to adopt was submitted to the same judge on the same day.
I commend you and your wife for wanting to rescue these little ones. I wish you the same success that we had.
(My husband has reminded me that our process wasn't really painless. There were lots of snags and SNAFUs, too many reports to make, and more than a few lines to stand in. I guess it's a bit like labor pains -- when it's over, you forget just how difficult it was! 
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