The documented MS C RTL quoting rules (that not all Win32 programs follow, unfortunately) say that to get <bar " baz> you should write <"bar \" baz">. The implementation is a bit weird, especially if you don't follow those rules. But your case doesn't work for me:

C:\> perl -le"print '<',$_,'>' for @ARGV" "foo "" bar"
<foo ">
<bar>

C:\>
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Note that \ only "escapes" when in a construct matching /\\+"/ (an even number of backslases results in $n-1 backslashes, an odd number in $n-1 backslashes followed by a quote).

This pointed out a subtle bug in the "current" Perl quoting that is done:

system(
    $^X,
    '"-leprint qq(<$_>) for @ARGV"',
    "\\root\\subdir\\",
    "\\root dir\\sub dir\\",
);

produces:

<\root\subdir\>
<\root dir\sub dir">
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The fact that I had to quote and be careful with that second argument is the not-subtle short-coming. But the fix for it also fixes the final \ turning into a ".