It's a long shot but I've been caught out before with self-edited Makefiles fumbling the removal of binaries from the build directory, being skipped by make and, if I'm wrestling with cross-compilation, ultimately causing the linker to complain about unrecognised format. I also used to see that after the laptop crashed, leaving truncated .o files in the build directory. What you're describing suggests that the secp256k1 code is being natively compiled when it should be cross-compiled. I've also encountered crypto files that need to be compiled with plain C, requiring ${CC} to be properly bound to the corresponding MXE binary.

Cheers

Graham