labeas - I really think you are a candidate for using YUMI-UEFI multiboot for your project. There is the original YUMI, and the more recent YUMI-UEFI. I would choose the newer version for your Aptio.
You've already paid your Microsoft-tax, perhaps many times over your lifetime like all of us purchasing computers with dos or windows pre-installed. What better way to get back some of your investment by using a GPL'ed windows tool to get your troublesome setup going.
I've gone into depth about it here:
http://forum.tinycorelinux.net/index.php/topic,23010.msg143982.html#msg143982But if you want the checklist approach, here it is.
1) Download the Tinycore iso(s) you want to boot from the Windows box.
2) Use YUMI-UEFI to burn the iso(s) to your usb stick.
3) Copy and paste the cde directory to the root directory of your usb stick.
4) Rename this cde directory in the root, to tce.
5) Find the grub.cfg file in the TinyCorepure64 directory. Don't mess with other grub files earlier in the path, as they pertain to YUMI itself.
It can be found here:
/mnt/sdaX/multiboot/TinyCorePure64-10.1/EFI/BOOT/grub/grub.cfg
6) Change the reference in the TC and TCW subsections from "cde" to
tce=LABEL=MULTIBOOT
This should serve as a guideline if you want to run the 32 bit version, although I have not done so.
Note that I don't use the multiboot feature. But if you do, you may not want to share a tce directory. In the case you are multibooting say 64 bit and 32 bit, you might want to have tce64 and tce32 directories in the root. Change your grub.cfg to point to those accordingly.
Of course, the stick is fat32. NOT exFAT, but fat32. Maybe you are ok with that. If not, then you'll have to dig harder with a manual install.
Maybe this will relieve some of the problems. And don't forget - back in 1992, I had already purchased MS-DOS many times over retail, and used RAWRITE.EXE inside dos to create the boot/root/userland floppies for Slackware. Trying to remember if I paid for mbasic-80 on my CP/M machine or if it was part of the "tax" even back then.
So I'm not defending Microsoft and their actions, but I am merely saying, you like most of us, have already paid $$$ in ms taxes. Maybe make use of it with a clearer conciousness with YUMI?