I did the job myself now. Giving a residence address in New Zealand, I submitted an application for a single-entry tourist visa and quite promptly received the payment request for "300 NZD" from the "Royal Thai Embassy, Wellington", but I won't make that payment, of course, because I don't like the price.
I can't give a link to that page because it is personalised to my logged-in account, but I am proud to give below a screenshot of it.
That's the confirmation I had been seeking, now we have it.