You need to install the Japanese game first, then patch it with the noDVDpatch, then those NEW files that are added to the root folder, copy those and put them somewhere. Then use the mirrormoon patch. After that's all done copy those files you patched with the noDVDexe back into the root folder.
Unless there's some easier way to do this. The noDVDpatch couldn't find the utaware-dvd.exe when using the mirrormoon installer directly, without using it to patch a Japanese install when I was installing it.