Instead of a non-greedy qualifier, you can use a negative look-behind assertion to get your replacement right. (See perlre)

$xml =~ s#\t<element attribute='$name'>(?:.(?<!</element>))*</element>
+\n#$node#s;

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Side note: the /s modifier is not needed here.

In reply to Re: limiting regular expression greediness? by Caron
in thread limiting regular expression greediness? by Anonymous Monk

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