However, since newlines are present, I have to OR with something that matches them

Not sure I understand. Normally, /s is sufficient for "." to also match newlines. No alternation required.

my $text = "<Master ID='42' NameU='foo\nbar'";

if ($text =~ /<Master ID='.*?' NameU='(.*?)'/s) {
    print "'$1'\n";
}
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outputs (as expected)

'foo
bar'
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