Lets pretend we've got a $5000 budget.
Quick back-of-the-envelope math shows that a 8xGTX1080¹ box will be able to generate ~3 onion addresses beginning with "nytimes" every second, we can afford 6.25 months of this.
Instead of waiting a really long time, we'll rent multiple boxes and squeeze all that into one month. In that month our servers will find approximately 44055283.1 onion addresses beginning with "nytimes".
At least with the wordlist² I use, without a prefix I discover approximately one "good" onion per 8 million random onions. Considering we've got a 7 character prefix for our 44 million onion candidates, so I'd expect a significantly better rate than just 1/8000000
So yeah, in a month you'd probably find at least 5 "better" onion addresses.
¹ $800 a month https://selectel.com/solutions/gpu/ Shouldn't be a problem for NYT to get a few of these.
² which besides words contains some easily memorable fillers such as "aaa" "bbb" and so on