We put forward a new algorithmic solution to the massive unsourced random access (URA) problem, by leveraging the rich spatial dimensionality offered by large-scale antenna arrays. This paper makes an observation that spatial signature is key to URA in massive connectivity setups. The proposed scheme relies on a slotted transmission framework but eliminates the need for concatenated coding that was introduced in the context of the coupled compressive sensing (CCS) paradigm. Indeed, all existing works on CCS-based URA rely on an inner/outer tree-based encoder/decoder to stitch the slot-wise recovered sequences. This paper takes a different path by harnessing the nature-provided correlations between the slotwise reconstructed channels of each user in order to put together its decoded sequences. The required slot-wise channel estimates and decoded sequences are first obtained through the hybrid generalized approximate message passing (HyGAMP) algorithm which systematically accommodates the multiantenna-induced group sparsity. Then, a channel correlation-aware clustering framework based on the expectation-maximization (EM) concept is used together with the Hungarian algorithm to find the slotwise optimal assignment matrices by enforcing two clustering constraints that are very specific to the problem at hand. Stitching is then accomplished by associating the decoded sequences to their respective users according to the ensuing assignment matrices. Exhaustive computer simulations reveal that the proposed scheme can bring performance improvements, at high spectral efficiencies, as compared to a state-of-the-art technique that investigates the use of large-scale antenna arrays in the context of massive URA.