You can build Julia from source with mingw but direct the build system to use an mkl library instead of building openblas from source. At one point mkl on windows didn't export gfortran style naming conventions for blas and lapack functions, but recent versions do last I checked. Could even be able to switch from an existing Julia binary by rebuilding the system image.
I think that linker error is from arpack. Try making a copy of mkl_rt.dll called libmkl_rt.dll and see if that helps. libtool isn't able to link against dlls that don't have a lib prefix unless you have a corresponding .dll.a import library (maybe copying and renaming one od the .lib files to libmkl_rt.dll.a could also work?) because being annoying is what libtool does.
libmkl_blas95_ilp64.alibmkl_blas95_lp64.alibmkl_core.alibmkl_core_dll.alibmkl_intel_ilp64.alibmkl_intel_ilp64_dll.alibmkl_intel_lp64.alibmkl_intel_lp64_dll.alibmkl_intel_thread.alibmkl_intel_thread_dll.alibmkl_lapack95_ilp64.alibmkl_lapack95_lp64.alibmkl_rt.alibmkl_sequential.alibmkl_sequential_dll.alibmkl_tbb_thread.alibmkl_tbb_thread_dll.a
1033/mkl_msg.dlllibimalloc.dllmkl_avx.dllmkl_avx2.dllmkl_avx512.dllmkl_avx512_mic.dllmkl_core.dllmkl_def.dllmkl_intel_thread.dllmkl_mc.dllmkl_mc3.dllmkl_rt.dllmkl_sequential.dllmkl_tbb_thread.dllmkl_vml_avx.dllmkl_vml_avx2.dllmkl_vml_avx512.dllmkl_vml_avx512_mic.dllmkl_vml_cmpt.dllmkl_vml_def.dllmkl_vml_mc.dllmkl_vml_mc2.dllmkl_vml_mc3.dll
floatfuncs.jlPlease submit a bug report with steps to reproduce this fault, and any error messages that follow (in their entirety). Thanks.Exception: EXCEPTION_ACCESS_VIOLATION at 0x0 -- unknown function (ip: 0000000000000000)unknown function (ip: 0000000000000000)*** This error is usually fixed by running `make clean`. If the error persists, try `make cleanall`. ***make[1]: *** [Makefile:200: /c/users/zpan/Documents/GitHub/julia/usr/lib/julia/sys.o] Error 1make: *** [Makefile:69: julia-sysimg-release] Error 2
Before you spend too much time on this, how sure are you that MKL will make a major difference over openblas on your application? openblas is close in performance to MKl on many, but not quite all operations. In some cases it may even be faster. Open source Julia is much better supported against openblas, especially on Windows. There are avenues for commercial supported Julia as well.
Julia Computing offers custom solutions that aren't necessarily listed on the products page of our website yet, you can inquire at the contact address there.