As a native, I find modern MSA and CA very interrelated. The difference is that CA is far complex as many words are not used today. I really like your enthusiasm regarding CA, which is really difficult for most learners, and throughout my teaching experience of MSA on YouTube, I find that MSA is of ultimate interest for most of the Arabic-language seekers. Many learn MSA to understand the Quraan despite being in CA, which is possible because learning MSA, gives you almost 70% of the understanding of the Quraan text.
If you want to dig into CA, it is far more difficult I guess, but not impossible. I remember some good books about this but need to make sure. I will come back if found any - sheers