@j0natr0n I also have a beelink ap34, and over the past 4 days I have been working on getting Batocera working on the device. As of now I have it working fully with no issues. To get it to boot you need to use a 32bit bootloader, I used rEFInd, I can give you the bootloader folder I used and you can simply replace the one on the USB.
If you want to install Batocera on your embedded eMMC storage then you will need to either build Batocera yourself via buildroot with some changes to the config files so that the build uses kernel version 4.12, as 4.10+ is needed for the eMMC in the AP34, and Batocera is currently using 4.9. Also some changes are required to the kernel config itself to build in the eMMC modules. I did run into a couple snags during the build that I could help you with if you also run into them.
If your not comfortable building yourself I can give you a link to download the image I made.