Even if you want to write all the code yourself (which is a fine decision), the only reason in 2026 to bang your head against a problem like this for 20 hours is if you really enjoy doing so.
(I'm surprised that "earlier AI models" didn't work for the author. For me, free-tier Gemini gets stuff like this correct all the time.)
One reason I realized recently - when you work it through with an LLM you get full process history linearly serialized, the back and forth, thinking traces, web lookups.
When I need to get back into the task it's much easier to get back in to "the flow".
I think it'll be common practice to start commiting agent logs with the code pretty soon.