So I actually ended up flashing only the system and boot img files, and that let the device turn on. There were a few problems I ran into, though. Settings kept force quitting, for one thing. But I was able to make a fresh Helium backup, so then I wiped everything and started over. After spending a bit of time restoring some files, my One is running well again. Thank both of you so much for your help! @sir_brickalot @HasH_BrowN

So, I actually ended up flashing only the system.img and boot.img files, and that let the device turn on. 

There were a few problems I ran into, though. Settings kept force quitting, for one thing. But I was able to make a fresh Helium backup, so then I wiped everything and started over. After spending a bit of time restoring some files, my One is running well again.