This depends upon where you are in the start-up continuum. If you are still in search of a viable business model (i.e. the start-up phase) then the "multiple hats" scenario is spot on. In this phase the key is to discover that which is repeatable and scalable. In other words - to put your energy...
VP of Logistics? Executive Officer Of Planning and Projects? And if you are concerned that one person can do it all there is the possibility to hire one as the senior exec with a secondary as junior exec.
No. The only way this could work is by outsourcing the people to other companies. But this would change the business you're in and you might as well just outsource the department to a company who does this already. If recommend reading a book called "The Goal" - it explains things better than me.
I don't think it is what you are looking for, but MailChimp.com was created by mistake from a services agency. They were sending emails for their clients and the next thing you know, they were making most of their money from send costs and the rest is history. Sorry I can't be more help.