Why would you go through the work of trying to get the build working on another system? When you said you were building on “Linux” in your original post, I thought you meant the OS running on the Intel Atom.
I’m curious to understand where you’re coming from because I’ve set up enough GCC and Keil toolchains to not even think about trying to replicate them for Klipper when somebody has done the work already (and validated the output). It seems that it would be quite a bit of work with a marginal, at best, improvement in speed (I don’t think there’s anything else you gain).
Personally, I think building the firmware image on the host is quite inspired although the suggested approaches of putting the firmware onto an SD Card are less than elegant, which is why I came up with the SDL script: