What about the idea of initializing the random pool from some entropy that was saved to a file on the previous boot?

Before the first boot, the entropy file could be initialized by the installation system.

Yes, these entropy files could be compromised, but that would be no worse than compromising the kernel binary or any number of other sensitive files. So as long as you have trust in the security of the most sensitive files on your filesystem, adding another sensitive file should not be much of a concern, as long as it's protected properly.