I see what you are faced with now. This is a bit more complex than I initially imagined myself as well.
I am going to mention this straight out at the onset of this and I may have to tell you that perhaps Antergos is just not set up for how your custom system is. Though, in having said that, it should be because as technology changes, so do (and should Operating Systems).
So maybe the Antergos devs are just not there yet at this point in time.
Please read this,
I went to the Arch Wiki (UEFI wiki page) and read this:
On some UEFI systems the only possible way to launch UEFI application on boot (if it does not have custom entry in UEFI boot menu) is to put it in this fixed location: /EFI/BOOT/BOOTX64.EFI (for 64-bit x86 system)
In having just posted/quoted that, what is supposed to happen is that your firmware is supposed to read the boot manager’s data and then determine which UEFI application is to be launched (you have 3 you mention). Apparently, that is not happening.
And because you cannot even boot live with Antergos, most obviously you cannot even do a simple task such as
cp /path/toEFI/grubx64.efi /path/to/efi/shellx64.efi to allow yourself to get started.
Finally, you seem to have all the other ingredients correct for initially wanting to use Antergos prior to starting it as a Live CD.
I have to tell you that at this point, I would be stumped. I do not know where to go at this point to further help you. A process like this might be quite exhausting. Too time consuming and to be honest, I think it’s also important to ask yourself if the exhaustion and strength of effort are necessary just to get an operating system going.
This is beyond my knowledge base and I would rather that someone with more experience follow through with this, then.
If you prefer the real Arch, go ahead. Best of efforts to you.
I should also tell you that there are other rolling releases out there and they DO NOT include Manjaro, like what some people might like to use.
I also use Chakra – Arch based. Has own repos that, that system uses.
KDE is default. Stable too. chakra linux
Am only mentioning this if you are looking for something other than Manjaro and true Arch.
Bridge LInux too. bridge linux