Text de-identification techniques are often used to mask personally identifiable information (PII) from documents. Their ability to conceal the identity of the individuals mentioned in a text is, however, hard to measure. Recent work has shown how the robustness of de-identification methods could be assessed by attempting the reverse process of _re-identification_, based on an automated adversary using its background knowledge to uncover the PIIs that have been masked. This paper presents two complementary strategies to build stronger re-identification attacks. We first show that (1) the _order_ in which the PII spans are re-identified matters, and that aggregating predictions across multiple orderings leads to improved results. We also find that (2) reasoning models can boost the re-identification performance, especially when the adversary is assumed to have access to extensive background knowledge.