Here's a couple things I've seen be problematic in the fashion you're describing.
Are you able to open task manager on the device while it is hung?
Is HIIClient running (memory fluctuating)?
If yes, it's possible it's just chugging away processing, though the explorer crash is weird.
How large is your HII library?
I have seen library's that were huge, and basically cause things to go pretty slow. I don't have a threshold of size, but it's something to consider.
As a test you could go make a new folder, point your HII library at that folder (so it's got no drivers to actually use/load) and run your template again.
This would do 2 things:
1. Identify if it's something with the action/template that is problematic
2. Identify if it's the library itself causing issues
If the new empty library does not cause the issue I can think of 2 possible culprits
1. The size is large, and the task is slow
2. There is a driver getting laid down that is causing issues
If it's the former, you should see that in the task manager.
If it's the latter, you could look at the hiiclient log after a reboot to see what drivers got paired. From there it becomes a troubleshooting process of weeding out drivers to find the one that might be causing issues.
In this particular scenario my suspicion would be that HIIClient ran, paired drivers, put them in the LDDriverStore, and is trying to load them into windows (can't recall the process that loads them when it's in windows, but it's DISM when in WinPE).
At the bottom of the HIIClient log there should be a line indicating it calls something to actually load the drivers, I think there might be a corresponding log with that process.
As I write this, this scenario actually sounds pretty plausible since your experiencing the explorer crash only on this model....
This problem was never resolved. Since we retired all our E 6400 Laptops the situation cured itself.