Spoofing is a serious threat to the widespread use of Global Navigation Satellite Systems (GNSSs) such as GPS and can be expected to play an important role in the security of many future IoT systems that rely on time, location, or navigation information. In this paper, we focus on the technique of multi-receiver GPS spoofing detection, so far only proposed theoretically. This technique promises to detect malicious spoofing signals by making use of the reported positions of several GPS receivers deployed in a fixed constellation. We scrutinize the assumptions of prior work, in particular the error models, and investigate how these models and their results can be improved due to the correlation of errors at co-located receiver positions. We show that by leveraging spatial noise correlations, the false acceptance rate of the countermeasure can be improved while preserving the sensitivity to attacks. As a result, receivers can be placed significantly closer together than previously expected, which broadens the applicability of the countermeasure. Based on theoretical and practical investigations, we build the first realization of a multi-receiver countermeasure and experimentally evaluate its performance both in authentic and in spoofing scenarios.