Build Makefile C++ project without configure to WASM using Emscripten - c++

Question

I want to compile this C++ project to WASM using Emscripten. For this, I am following the documentation on building projects.
The project only has a Makefile, no Configure or CMake. It should be portable from what I can tell, and the project compiles fine using regular make, as described in the Readme.
Because there is no configure file, I skipped the emconfigure step. The documentation says that I have to edit the Makefile manually in that case, but I can't get it right.
Running emmake make works, and produces .o files in the bin directory, and an executable. This produces the same result as running make normally, from what I can tell. Both executables can be executed as normal (./zilch).
Running emcc bin\main.o is where I get issues though:
wasm-ld: error: unknown file type: bin/main.o
emcc: error: '/home/johannes/emsdk/upstream/bin/wasm-ld -o main.wasm bin/main.o -L/home/johannes/emsdk/upstream/emscripten/cache/sysroot/lib/wasm32-emscripten -lGL -lal -lhtml5 -lstubs-debug -lnoexit -lc-debug -ldlmalloc -lcompiler_rt -lc++-noexcept -lc++abi-noexcept -lsockets -mllvm -combiner-global-alias-analysis=false -mllvm -enable-emscripten-sjlj -mllvm -disable-lsr --import-undefined --strip-debug --export-if-defined=main --export-if-defined=__start_em_asm --export-if-defined=__stop_em_asm --export-if-defined=__main_argc_argv --export-if-defined=fflush --export=emscripten_stack_get_end --export=emscripten_stack_get_free --export=emscripten_stack_get_base --export=emscripten_stack_init --export=stackSave --export=stackRestore --export=stackAlloc --export=__wasm_call_ctors --export=__errno_location --export-table -z stack-size=5242880 --initial-memory=16777216 --no-entry --max-memory=16777216 --global-base=1024' failed (returned 1)
Running file bin/main.o shows: bin/main.o: ELF 64-bit LSB relocatable, x86-64, version 1 (SYSV), with debug_info, not stripped. Running emmake clearly still compiled it to x86, not wasm.
In the flags.mk file that is imported into the Makefile, the CC variable is set to g++. Changing it to em++ gives this error:
em++: error: Passing any of -msse, -msse2, -msse3, -mssse3, -msse4.1, -msse4.2, -msse4, -mavx, -mfpu=neon flags also requires passing -msimd128 (or -mrelaxed-simd)!
But adding this to CFLAGS in flags.mk only throws another cryptic error message:
em++: error: '/home/johannes/emsdk/upstream/bin/clang++ -target wasm32-unknown-emscripten -fignore-exceptions -fvisibility=default -mllvm -combiner-global-alias-analysis=false -mllvm -enable-emscripten-sjlj -mllvm -disable-lsr -DEMSCRIPTEN -D__EMSCRIPTEN_major__=3 -D__EMSCRIPTEN_minor__=1 -D__EMSCRIPTEN_tiny__=18 -Werror=implicit-function-declaration -I/home/johannes/emsdk/upstream/emscripten/cache/sysroot/include/SDL --sysroot=/home/johannes/emsdk/upstream/emscripten/cache/sysroot -D__SSE__=1 -D__SSE2__=1 -D__SSE3__=1 -D__SSSE3__=1 -D__SSE4_1__=1 -D__SSE4_2__=1 -Xclang -iwithsysroot/include/compat -O3 -g3 -Wall -fmessage-length=0 -fopenmp -maes -mtune=native -mrelaxed-simd -std=c++11 -Isrc -I/mnt/c/Users/johan/source/repos/Zilch/Zilch/framework/gadgetlib/gadgetlib/../. -I/mnt/c/Users/johan/source/repos/Zilch/Zilch/libstark/src -I/mnt/c/Users/johan/source/repos/Zilch/Zilch/algebra/algebralib/headers -I/mnt/c/Users/johan/source/repos/Zilch/Zilch/algebra/FFT/src -I/mnt/c/Users/johan/source/repos/Zilch/Zilch/framework/zilch/src -c /mnt/c/Users/johan/source/repos/Zilch/Zilch/framework/zilch/main.cpp -o /mnt/c/Users/johan/source/repos/Zilch/Zilch/bin/main.o' failed (returned 1)
I also tried to replace every $(MAKE) with $(EMMAKE) in the Makefile without success.
I am aware that I probably have to convert the project to CMake, or include a Configure file, as the documentation says. But I can't figure out for the life of me how that should look. If it isn't obvious, I am not experienced with any of these tools, so please be kind if I'm missing something super obvious.