Hi JC,
I'm not sure how much help I can be, but I'll try. Out of state child support enforcement, from what I understand, is a rather tedious process. That doesn't mean you won't see your money, but it will take some work to see it in any reasonable amount of time. A few stories I've read of involve a large sum paid out 20 years later after a large injury settlement, or asset liquidation. But, don't let that discourage you. There is a federal law called the Interstate Family Support Act or something similar. This is what gives all states the ability to enforce a child support order from the originating state.
What I would do is start by calling the child support enforcement office of the father's state. Have a copy of your Kansas child support order in hand to be able to relay the KS case number and other information. The Income Withholding Order is they key document that tells the employer to withhold income from a paycheck. So, I think the first step would be to start a file with the father's new state telling them you are seeking a garnishment of his wages. See how much help they will give you.
Trying to locate his wages is the real issue typically. I have personally executed numerous subpoenas to obtain this information in KS with unbelievable success. I wish more people knew the power of a subpoena. The trouble is, out of state subpoenas can be tricky too. So, the best way is to use a process server in the father's state or simply hire an attorney in that state to take care of it. They would locate the father's residence and subpoena his last known employer. This usually gives a solid paper trail so you know where to look next. For instance, you might subpoena income records, employment application, resume, and work performance history. Based on this, you could learn what jobs were held previously and learn what the wages were. You could also learn more about what types of jobs are held based on skill set.
Armed with this information, you could then do "employment verifications" with any businesses you think he might work at. There are also plenty of public records that could be had as well to learn of these kinds of things.
You could always just exercise your right to discovery and file a "request for production" of documents directly to him if you know his address (or even his last known address). This would give him 30 days to produce his income records or he would be in contempt.
Hopefully that helps a little. I'm sure it will be a rather tedious process and I really think hiring an attorney in the district you know him to be in would be the easiest for you. You can't really do much from KS since he's moved out of state.