A snap can either be run as root manually by a user via sudo or similar, and it can declare a daemon which will then run as root. So I don’t think classic should be needed for this use-case to run as root.
Can you please provide more information? In particular, what errors do you encounter when running under strict confinement?
Finally, if you still think classic confinement is required, can you please detail which category of application your snap first within as per the Process for reviewing classic confinement snaps? Thanks.