Hi,
Below will be some comments on regards of your questions:
I understand that you compiled the code successfully for headless mode functionality using LLCE v1.0.5 QLP1 software, is that correct?
[DA]: We are able to get the *.elf file, yes.
Where can I find the LLCE v1.0.5 QLP1 software? I only found the LLCE v1.05 version software on the NXP official website.
[DA]: QLP1 is provided on a different option, not under the same v1.0.5. You could confirm if it is available to your account under the previous menu that you are showing:

If it is not available, help us contacting your local NXP FAE/DFAE/representative, for them to enable your account (if available).
Please, let us know.