In other news, now that I’m all done, I started my rewatch from scratch. But since I was in a Tales of the Jedi mood, I watched all of Dooku’s TOTJ episodes first, and then my two prologues, then into TCW:R proper.

And I’ve gotta tell you, that ordering - chronological (minus Ahsoka’s intro), but skipping the two first prequel movies, really works. Benefits:

The Dooku episodes do such a great job of introducing the viewer to the whole Star Wars setting. They’re powerful, beautiful, character-driven, and explain the state of the galaxy really clearly. Even without seeing the movies, you understand why many planets would want to leave the Republic, and why Dooku would be a fitting figurehead.
The whole, this way, is way more focused on high quality character development, and the non-movie content does a really good job of filling in the gaps as you go. They feel like stories with worldbuilding, rather than the prequel movies’ worldbuilding with stories in them.
Anakin’s introduction is carried by the Tartakovsky series, and it totally works. We get this nice throughline of Dooku > Qui-Gon > Obi-Wan > Anakin. Dooku 's become our focal villain (after his great and understandable development) and then hiring his few right hand characters, then Anakin is introduced as a brash but great Jedi whom the Jedi Council regard as the ‘chosen one’ and the Sith have a particular interest in. He’s a great pilot with a secret wife, and his character is clear - and in his introductory episode we see via his clash with Ventress how he’s tempted by the dark.
We then see Ahsoka’s introduction, and she’s cemented as his apprentice as their character and relationship comes more into focus over the first couple of TCW:R episodes.
Seeing Mandalore early also does a great job of introducing third parties - and its neutrality also brings the corruption of the Republic into sharper focus.
Speaking of which, the Republic’s corruption is far clearer here - yes, it’s probably a force for good, and stability, but we understand much better why people might object to it, and why it’s exploitable by Sidious. We also see Mace Windu as much more representative of the Jedi as the [corrupt] Republic’s tool, rather than a wiser questioning presence like Dooku, Qui-Gon, or Yoda.

The only things really missing from watching it this way are seeing the Obi-Wan/Maul plot start (you could maybe watch TPM as a flashback before the nightsisters arc?) and more detail on the clones/Jango/Boba (you could maybe watch AOTC between seasons one and two, after we see Kamino but before we see Boba seeking revenge on Mace).

Anyway, it makes for interesting viewing!