I only want Ubuntu (actually LM), no dual boot on this machine, and only 32bit Linux at that (though the machine is capable of 64bit and UEFI).

Why 32 bit? I've had flaky behavior with 64bit LM (17.2), and found once before (another Asus) that the problems went away after switching to 32bit (same LM 17.2 using same home dir.). Previously Windows was installed (came with the machine). At the time, I wiped windows off and I did a 64bit LM 17 install successfully on this machine with UEFI still on. But as I said, I want 32bit if I can get it.

There are BIOS switches for on the machine to disable UEFI stuff ("CSM") and "fast boot", and "Secure Boot" was already disabled. With these switches actvated to disable UEFI, I was able to build and boot a USB with a 32bit LM 17.2 (using usb-creator-gtk) to boot and install LM 17.2 over the 64bit LM 17.2 partition I had before. The install went OK (though it first demanded a "grub-bios" marked partition as the first partition on the disk (which I created using gparted). I then ran boot-repair after the install completed to make ensure I had a bootable system. (I also made sure on Boot Repair options that "use uefi partition" was unchecked.) And with the boot usb running, I can click "Computer" and see the LM 17.2 32bit partition and my /home partition. No problem.

However, the machine is unbootable. After powerup, the machine goes straight into setup (BIOS/UEFI setup). There's nothing listed in the "boot order" page of the BIOS, only a sinister message asking me if I want to add a UEFI bootable partition, which makes me think that although UEFI is supposedly off, the BIOS will still only recognize UEFI partitions. (PS I updated to the latest Asus BIOS for the X200ma before starting all this).

Some questions: 1) is it even possible to install a 32bit OS on a UEFI system, even if UEFI is supposedly turned off and you're in legacy BIOS mode. 2) Do I need to do something with UEFI in order to boot?

If it will help, here's the boot-repair output....

http://paste2.org/sw5bLD3C

PS: In the USB install, I chose "something else", because I already had an LM partition, a /home partition, and a swap partition existing on the disk---so I didn't really install "from scratch".

Some braindead BIOSes require boot flag activated when booting GPT disks. There is protective MBR even on GPT disks, you can use fdsik and activate the boot flag on your boot partition.

The boot flag wasn't set for the LM 17.2 partition, so I set it but still no boot or even listing the partition in the boot list (empty) of it. Maybe if I buy a gun and threaten to shoot a hole in UEFI?

I'm just guessing that despite disabling UEFI, the firmware still looks for something in UEFI space for the start of the grub boot menu. I haven't a clue of the order of events when a UEFI disabled system tries to boot in legacy mode. Or where boot-repair puts the grub menu. (I would presume in the same old place, as long as you tell it "legacy boot".)

As Emerson noted, there is a protective MBR on GPT disks. This is basically a "fake" MBR that is used when someone wants to install the OS in non-UEFI (legacy) mode.

I am sure you are aware that a 32 bit OS can only be installed in legacy mode, with rare exceptions. Here is what Rod Smith has to say about that:
"Ensure that you're using a distribution that's the right bit depth/ EFI runs boot loaders that are the same bit depth as the EFI itself. This is normally 64-bit for modern computers, although the first couple generations of Intel-based Macs, some modern tablets and convertibles, and a handful of obscure computers use 32-bit EFIs. I have yet to encounter a 32-bit Linux distribution that officially supports EFI, although it is possible to add a 32-bit EFI boot loader to 32-bit distributions. (My Managing EFI Boot Loaders for Linux covers boot loaders generally, and understanding those principles may enable you to modify a 32-bit distribution's installer, although that's not a task for a beginner.) Installing a 32-bit Linux distribution on a computer with a 64-bit EFI is difficult at best, and I don't describe the process here; you should use a 64-bit distribution on a computer with a 64-bit EFI."

You can reformat your hard drive to msdos partitioning instead of GPT, to make things simpler. Or you can install to your GPT hard drive using this tutorial -
Legacy Mode Installation Using GPT Partitions