Is SSIS the right tool?
Maybe. Let's start with the numbers
600000 files / 60 minutes = 10,000 files per minute
600000 files / (60 minutes * 60 seconds) = 167 files per second.
Regardless of what technology you use, you're looking at some extremes here. Windows NTFS starts to choke around 10k files in a folder so you'll need to employ some folder strategy to keep that count down in addition to regular maintenance
In 2008, the SSIS team managed to load 1TB in 30 minutes which was all sourced from disk so SSIS can perform very well. It can also perform really poorly which is how I've managed to gain ~36k SO Unicorn points.
6 years is a lifetime in the world of computing so you may not need to take such drastic measures as the SSIS team did to set their benchmark but you will need to look at their approach. I know you've stated the hardware is outside of the scope of discussion but it very much is inclusive. If the file system (san, nas, local disk, flash or whatever) can't server 600k files then you'll never be able to clear your work queue.
Your goal is to get as many workers as possible engaged in processing these files. The Work Pile Pattern can be pretty effective to this end. Basically, a process asks: Is there work to be done? If so, I'll take a bit and go work on it. And then you scale up the number of workers asking and doing work. The challenge here is to ensure you have some mechanism to prevent workers from processing the same file. Maybe that's as simple as filtering by directory or file name or some other mechanism that is right for your situation.
I think you're headed down this approach based on your problem definition with the agent jobs that handle N files but wanted to give your pattern a name for further research.
I would agree with Joe C's answer - schedule the SQL Agent job to run as frequently as needed. If it's already running, it won't spawn a second process. Perhaps you're going to have multiple agents that all start every minute - AgentFolderA, AgentFolderB... AgentFolderZZH and they are each launching a master package that then has subprocesses looking for work.