Why do you want a classical education, for its own sake/merits, or because it sounds good?
If the former, go for it. If the latter, there are better things to do with your time (whatever naturally interests you). A classical education is constraining in the same way a formal education is constraining. There's nothing inherently valuable about muh dead language or muh old book that makes it more worthwhile than learning other things, like Spanish vs Latin, Sengoku Jidai versus the late Republic, "classical music" vs jazz, "literature" versus novels in general, etc.
Just study what you want to study, regardless of if it matches up with some program. But make a point to actively study. I try to read about 60 pages of nonfiction a day, and rotate through three books. It's pretty lopsided because it's almost always history, I don't read much science or other stuff, but I do play an instrument (saxophone) and am learning another one (fiddle/violin). I plan to try to get into painting. It's self-cultivation, but it's not tied to what a university hundreds of years ago would have thought was important. I don't really study anything practical (besides cooking), but learning practical skills would be even better, like picking up shit like gardening or beekeeping or chickens or whatever. To me, the big thing is to make an effort to be a well-rounded person. Classical education has an element of that, but in some ways it sounds awful constraining.
I would suggest adding economics to your self-education (doesn't have to be to a real advanced level), and I don't know what mathematics is considered part of a classical education, but set theory is more important than anything else (all modern mathematics is built out of set theory) and game theory has lots of interesting applications, especially to politics. World religions, too.
This is getting off maybe into “this is important because I personally like it,” but other topics of interest are:
- Non-Euclidean geometries
- The mathematics of complex/imaginary numbers
- Astronomy, specifically big picture stuff like how the universe formed, how it will die, life cycles of stars
- Basic anatomy
- Knowledge of animals
- Knowledge of agriculture
- Traditional lifestyles/folk culture
- Any history that isn’t just the same worn out European/US history: Middle East, Africa, Asia, Native Americans and Mesoamericans/Incas