I think your word list is still considerably too large. Zero chance in my mind that jouk or qajaq, for example, would make it to the NYT wordlist. (I don't think they'd even be accepted in the crossword, which has looser standards, unless there was a very specific theme that called for them). Apart from being obscure, their only use seems to be as non-standard spellings, for juke and kayak respectively. The Spelling Bee doesn't even accept UK spellings.
At least 5 of the proposed pangrams wouldn't make the cut, either.
Perhaps you could scrape https://nytbee.com/, mentioned in the thread, for the historical answers, or contact the owner. Also @banana_giraffe, a commenter on this thread, seems to have scraped 6 years of data.
Then you could take a very permissive wordlist and filter it using the historical data. For all words of six distinct letters or fewer, you could determine whether they were allowed, not allowed, or indeterminate (no puzzle ever appeared that would have allowed them). My gut feeling is that you'd be left with very few indeterminate words, though jouk and qajaq might well be among them - review those manually.
At least 5 of the proposed pangrams wouldn't make the cut, either.