How can I print a string (single-quoted) containing double-backslash \\\\ characters as is without making Perl somehow interpolating it to single-slash \\
The only quoting construct in Perl that doesn't interpret backslashes at all is the single-quoted here document:
my $string1 = <<'EOF';
a\\\b
EOF
print $string1; # Prints a\\\b, with newline
Because here-docs are line-based, it's unavoidable that you will get a newline at the end of your string, but you can remove it with chomp.
Other techniques are simply to live with it and backslash your strings correctly (for small amounts of data), or to put them in a __DATA__ section or an external file (for large amounts of data).