I suppose I could make one of those addresses that are 1xxxxxxxxxxxxxxxxxxxxxx if you know what I mean.
1B1tco1nDustAddressDotComxxxntn2T
This also is a bad idea. Because you'd be creating new UTXOs that will remain in all nodes' memory forever without ever being spent. I'd say the initial address (where you had the private key) was better because at least that way assuming you received anything you' be eventually able to spend that output.
The better way, which was also already mentioned, is to use OP_RETURN and give all the satoshis to the miners as fee.