Do children's visa requirements for Thailand match those of adults in terms of financial proof?

I would contact the consulate you're dealing with to see if they'll issue 6 month METV's to children without financial proof.

Remember though children under 15 cannot be fined for overstay and children under 18 can't be banned for it. That's not saying they don't need a visa (because technically they do) but there are NO penalties for them if they overstay. Many people who come here with children get them a 30 day visa exempt stamp when they arrive and then let them overstay.

and what kind of visa are you going to get for yourselves and the children?