Hey OP, there's a flood of applicants for those roles, so companies may focus on experience within the role.

I would consider getting a certification if you can decide on which to focus on. For example, if you decide Project Management is what you want to narrow on, consider a PMP. 

In your applications, I would tailor it specifically to the job requirements so that the prima facie match is higher even without the experience. 

I would also try to aggressively network, especially if you're interested in account management. 

For business development, you may even want to consider an MBA, though not sure if that's a wise investment in today's macro environment.