I am not aware of away to prevent the IAM/RBAC roles from being excluded at specific resource levels.
You would need to move the Subscription holding the storage account to a new management group, excluding the permissions.
Adjust the permissions of that management group, to prevent storage account read access.
FYI: I looked into Deny Assignments as well (https://learn.microsoft.com/en-us/azure/role-based-access-control/deny-assignments) but this is for Blueprint created resources, not entirely for your usecase.
"You can't directly create your own deny assignments."