Can I deduct vehicle registration fees both under Schedule A and as a Schedule C vehicle business expense?

No, that is double dripping.  And if you deduct on Schedule C, it must be a vehicle with qualifying business use.

You can deduct the vehicle registration fee based on the percentage of the business related portion percentage on your schedule C, and to the personal portion percentage on your schedule A, but not to exceed 100% of the total vehicle registration expense fee for the vehicle for the year being filed