Is there any way to see the high level calculations behind CA state taxes, similar to how you can review for federal?

Yes.  You may do a State Review and preview your California State income tax return.  To do a state review:

1. In Tax Home Screen, click State.
2. Jump to State Review.
3. Under State review, it will display the error/s on your state income tax.
4. Click each review, it should take you to the line that had error/s.
5. Once fixed, you go back to State Review to check if it's ready to e-file.

To preview your 540 form:

• In Turbo Tax  Home Screen, select State: 
• Under State Return tab, click add a State.
• Click on Tax tools (left menu)
• Click on Print Center.
• Click on Print, save or preview this year's return.