Managed Payroll in an HCM platform ??[N/A]

We are small/midsize company with 4 offices in 4 states and about 60 employees. We are looking to move to a all in one solution from Paychex/BambooHR and all the other sites we need to log into. I had narrowed it down to Paycom/Paylocity & Rippling but then it became clear that management wants there to be a managed payroll component to this change. I don't currently run the payroll, I just report my teams info to the person who does. They will no longer be in the picture which is part of what has prompted this move. In the companies i have noted only Paylocity has a managed payroll option. Are there others I might have overlooked? One of my qualifiers is that it has to have an ATS and a LMS. I am an HR department of 1 over here and I manage all the things so I need a more efficient interface for myself and my employees. We can't keep going to 12 sites for basic information lol