The only distro I can find that successfully configures a functioning bootable GRUB on this (bastard) machine is Nobara, which looks very cool but is way too heavy! Some things are glitchy; attempting tab completion seems to freeze Konsole for ~5 seconds and does not complete the command as expected. We're working with an Intel Atom Z3735F@1.33GHz and 2GB RAM here.
How can a noob figure out what it's doing differently so I can apply that to Linux Mint Debian Edition or Crunchbang Plus Plus?
The weird thing is that once the system is installed, it does not seem to have what I think are the required packages for GRUB to be set up correctly with this type of UEFI.
To be brutally honest about this, your best bet is to recycle the unit.
The problems of trying to get a distro to install properly, have all the hardware working right and have a usable experience are not worth the minimal upsides.
I have an ASUS X205TA which is a similar unit and after trying for countless hours to get a usable device out of it was not going to be worth the headaches plus if I was getting paid for the time I spent on it I could have brought an off lease laptop with better specs.
I have had several distros working on the X205TA (I even had a how to guide written up on reddit years ago).
But I was not able to get a usable system (i.e. being able to use the system without waiting on average 20-120 sec for the device to process an action).
Life has gotten to the point that the effort to do so is better directed into activities that I would enjoy.