We present a synchronization transition study of the locally coupled Kuramoto model on extremely large graphs. We compare regular 405 and 1004 lattice results with those of 120002 lattice substrates with power-law decaying long links (ll). The latter heterogeneous network exhibits ds>4 spectral dimensions. We show strong corrections to scaling and mean-field type of criticality at d=5, while logarithmic corrections at d=4. Contrary, the ll model exhibits a non-mean field smeared transition, with oscillating corrections, suggesting the network heterogeneity is relevant, causing frustrated synchronization, akin to Griffiths effects.