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Analysis of late O-type stars observed in the Large Magellanic Cloud (LMC) by the VLT-FLAMES Tarantula Survey (VFTS) revealed a discrepancy between the physical properties estimated from model-atmosphere analysis and those expected from their morphological classifications. Here we revisit the analysis of 32 of these puzzling objects using new hydrogen-helium-silicon FASTWIND models and a different fitting approach to re-evaluate their physical properties. Our new analysis confirms that these stars indeed have properties that are typical of late O-type dwarfs. We also present the first estimates of silicon abundances for O-type stars in the 30 Dor clusters NGC 2060 and NGC 2070, with a weighted mean abundance for our sample of 7.05 +/- 0.03. Our values are about 0.20 dex lower than those previously derived for B-type stars in the LMC clusters N 11 and NGC 2004 using TLUSTY models. Various possibilities (e.g. differences in the analysis methods, effects of microturbulence, and real differences between stars in different clusters) were considered to account for these results. We also used our grid of FASTWIND models to reassess the impact of using the Galactic classification criteria for late O-type stars in the LMC by scrutinising their sensitivity to different stellar properties. At the cool edge of the O star regime the HeII 4686/HeI 4713 ratio used to assign luminosity class for Galactic stars can mimic giants or bright giants in the LMC, even for objects with high gravities (log_g > 4.0 dex). We argue that this line ratio is not a reliable luminosity diagnostic for late O-type stars in the LMC, and that the SiIV 4989/HeI4026 ratio is more robust for these types.