OP - It is silly to argue about what it all might mean. The answer is a phone call away. It also matters a great deal and parsing through the words won't help if the Consular officer simply says to OP, "it doesn't apply to your situation."

I would not rely on general information on the Consulate's website. Rather, I would call and ask whether in your specific situation, having had you e-visa rejected as the result of a criminal conviction, a third party agency may still represent you and whether it will be as effective as a personal appearance by you.

If a personal interview is required, then you have a choice to make. Either go to Houston and do it or abandon the trip.

If an agency may represent you, I would do some research. Ask around, make calls. Do not email. You are looking for a place which has at least handled situations such as yours.

To be frank, I do find it odd that the Consulate would permit a third-party agency which has never met the OP to take the place of an in-person interview given the reason for the underling e-visa denial.