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:\>
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">
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 ".