I note from Toto's website, that the original model flapper for the Drake toilet (THU331S) has been discontinued and replaced by a newer model with a different design (THU499S).
No, no, no. The flapper that comes in the toilet hasn't changed to the 499S,
the flapper that they want you to use as the replacement has changed to the 499S. For every toilet, regardless of what flapper comes in it. They got tired of stocking eight-million replacement flappers, and went to a universal one. That's the one that Terry doesn't like. They still use specific flappers in specific toilets at the factory.
They did the same thing with the fill valve, which was a success. Don't stock a million of them as replacements, just stock one Universal one. The toilet comes with whatever fill valve they put in it, but there is one universal replacement fill valve, which is basically a Korky 528MP, which Terry does like. That is the valve that Terry recommends (and uses a similar but more-expensive one, the Korky 528PRO, on his jobs).
I didn't read Terry to say that he doesn't like Korky flappers, just
that Korky flapper, the new Toto Universal one. The one that I recommended requires no flow adjustment; you just replace the old one with the new one and
voila! If that Red Korky Flapper for Toto is one that fits your toilet, then it's the easiest solution. (Tip: count the number of links in the chain on the one that's already attached, so you can get the chain length right the first time.) (Geek note: Toto did change the materials in some of the flappers that they are using in their toilets, but the good old THU331S/Korky 2021 (they are literally exactly the same thing in different boxes) works like a champ if it is the appropriate one for your toilet.