The simplest soln has to be NFS share the big disk.
Anything else is going to be less stable/reliable. Doesn't mean it won't be good enough, just not as good and def more complex.
If individual files are small enough (ie fit into small machine RAM easily), I'd consider multi-thread, 1 to listen to incoming stream, then Thread::Queue to output thread that sends file to big box.
This may seem a bit daunting if you haven't done threading, but it's not that bad.
Do you have some time in between each incoming file? If so, you may be able to do same thing (ie mem buff) without threads.
In theory, even without sufficient mem to swallow 1 file, you could still use the threading method.
Cheers
Chris