Recovering money owed by an unresponsive online business

I did business with an online business based in New Zealand, PredictIt, which has a firm in Washington, DC, called Aristotle, Inc., that handles their monetary transactions. I’m in California. They ended up owing me money, which they say they sent me as three paper checks by US mail. I received two of the checks, but the third one, for $814, never arrived. I contacted them through their help system and asked them to cancel payment on the lost check and issue a new one. They responded by saying that the request had been forwarded to the proper person. After several such queries and unhelpful replies, they have never paid me my money. It has now been a couple of months since I first reported the problem to them. I will owe income taxes on the money, and they’ve sent me tax forms as if they had paid me everything they owed.

Does anyone have any practical suggestions about how to recover money from an unresponsive business? I don’t think they’re fraudsters in general, or unable to pay — just disorganized.

I doubt that it would be practical to sue them in small claims court. I imagine the venue would have to be DC, and it wouldn’t make sense for me to fly to DC for this amount of money.

Should I send them a paper letter? If so, then what should such a letter say in order to be effective?

Is it possible that I could report this as credit card fraud, since I initially gave them money using my credit card?

If they are never going to pay me, how do I go about documenting this so that I at least don’t have to pay income taxes on the money that I didn’t receive?