The probes should create muliple staging areas.

How do you create a staging area outside of a galaxy? There wouldn't be enough matter or energy locally available to do anything useful.

In my opinion, a huge limiting factor is communication. How do you know if those probes reached their target?

Presumably you wait millions years for a return probe.

Because once you start the process, when and how would you stop it?

Indeed. These probes are going to be so far apart they are unlikely to be able to communicate with each other in any meaningful way.