trouble installing a Windows\System32 file to Windows\sysWOW64

Hi Experts, I guess this is a follow-up to my question from a week or so ago -
"My application's installation does not write files to \Windows\System32".
    In that question, I was having trouble installing files to a Windows 7 64-bit system using my old defunct installation software (www.install-us.de). I was informed about the free NSIS opensource installation software by Joe Winograd, so I've been learning that lately and thought I had created a successful installation script. I used the script here:

http://nsis.sourceforge.net/A_simple_installer_with_start_menu_shortcut_and_uninstaller

... as a template and it seemed to work fine - at least on my other 32-bit Win XP test desktop computer. I don't have a 64-bit machine here to test it on (my 32-bit XP laptop is my development computer), but I had a chance in the last couple of days to sign in to a user's 64-bit machine to test my script out and I ran into an error. Among other things, my app needs to install 3 files in the target user's System32 folder (or sysWOW64 for 64-bit machines):

mfc42.dll
msvcrt.dll
oleaut32.dll

But during installation on the 64-bit system, it generated this error window:

---------------------------
MyApp Setup
---------------------------
Error opening file for writing:

C:\Windows\System32\oleaut32.dll

Click Abort to stop the installation,
Retry to try again, or
Ignore to skip this file.
---------------------------
Abort   Retry   Ignore  
---------------------------


... when I checked his sysWOW64 folder, these files were there, but they may have already been there from before, as apparently they are fairly standard system files. Also, all my app's files were copied to the user's $INSTDIR folder correctly. Anyway, overall the installation failed as my app wouldn't run - I would assume because of this error message in one way or another. Would someone who is good with NSIS be able to help me out? I thought I did pretty much everything right - I have the requisite:

RequestExecutionLevel admin

...command, which allows privileges to Administrator-type systems.

And here's the relevant "install" section of my NSIS script:

section "install"
	# Files for the install directory - to build the installer, these should be in the same directory as the install script (this file)
	setOutPath $INSTDIR
	SetOverwrite on
	# Files added here should be removed by the uninstaller (see section "uninstall")
	file "MyApp.exe"
	file "MyApp.ini"
        file "testdata.txt"
        file "MyApp.ico"


	# Add any other files for the install directory (license files, app data, etc) here

        # Add Windows\System32 files here, these should NOT be removed by the Uninstaller
        SetOutPath "$WINDIR\System32"
        SetOverwrite ifnewer
        File "C:\WINDOWS\system32\mfc42.dll"
        File "C:\WINDOWS\system32\msvcrt.dll"
        File "C:\WINDOWS\system32\oleaut32.dll"
        SetOverwrite on
        File "C:\WINDOWS\system32\sortsol.dll"
        File "C:\WINDOWS\system32\SortSolX.ocx"
        ExecWait 'regsvr32.exe /s "$WINDIR\System32\SortSolX.ocx"'
        File "C:\Code-lock\Code-Lock.ocx"
        ExecWait 'regsvr32.exe /s "$WINDIR\System32\Code-Lock.ocx"'
        File "C:\Code-lock\zlib.dll"

 
	# Uninstaller - See function un.onInit and section "uninstall" for configuration
	writeUninstaller "$INSTDIR\uninstall.exe"
 
	# Start Menu
	createDirectory "$SMPROGRAMS\${APPNAME}"
	createShortCut "$SMPROGRAMS\${APPNAME}\MyApp.lnk" "$INSTDIR\MyApp.exe" "" "$INSTDIR\MyApp.ico"
        createShortCut "$SMPROGRAMS\${APPNAME}\Uninstall.lnk" "$INSTDIR\uninstall.exe"

	# Registry information for add/remove programs
	WriteRegStr HKLM "Software\Microsoft\Windows\CurrentVersion\Uninstall\${APPNAME}" "DisplayName" "${APPNAME}"
	WriteRegStr HKLM "Software\Microsoft\Windows\CurrentVersion\Uninstall\${APPNAME}" "UninstallString" "$\"$INSTDIR\uninstall.exe$\""
	WriteRegStr HKLM "Software\Microsoft\Windows\CurrentVersion\Uninstall\${APPNAME}" "QuietUninstallString" "$\"$INSTDIR\uninstall.exe$\" /S"
	WriteRegStr HKLM "Software\Microsoft\Windows\CurrentVersion\Uninstall\${APPNAME}" "InstallLocation" "$\"$INSTDIR$\""
	WriteRegStr HKLM "Software\Microsoft\Windows\CurrentVersion\Uninstall\${APPNAME}" "DisplayIcon" "$\"$INSTDIR\MyApp.ico$\""
	WriteRegStr HKLM "Software\Microsoft\Windows\CurrentVersion\Uninstall\${APPNAME}" "DisplayVersion" "$\"${PRODUCT_VERSION}$\""
	# There is no option for modifying or repairing the install
	WriteRegDWORD HKLM "Software\Microsoft\Windows\CurrentVersion\Uninstall\${APPNAME}" "NoModify" 1
	WriteRegDWORD HKLM "Software\Microsoft\Windows\CurrentVersion\Uninstall\${APPNAME}" "NoRepair" 1
	# Set the INSTALLSIZE constant (!defined at the top of this script) so Add/Remove Programs can accurately report the size
	WriteRegDWORD HKLM "Software\Microsoft\Windows\CurrentVersion\Uninstall\${APPNAME}" "EstimatedSize" ${INSTALLSIZE}

        MessageBox MB_OK "Click OK to reboot please"
          Reboot
sectionEnd

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Thanks!
    Shawn