Why has your organization built a one-size-fits-all ops organization if it doesn't have a one-size-fits-all dev organization? Sounds like a failure of ops organization to recognize that the needs of the email hosting guys are different from the website team or the billing team. Maybe you should build a set of smaller, more focused ops teams focused on meeting the needs of those different groups?
Smaller, more focused ops teams already exists, but are not bound by application boundaries but by system boundaries. (mostly, storage, compute and networking). The reason is because each of these is a completely different environment on its own.
