Recent studies have shown that vertical enthalpy transport can explain the inflated radii of highly irradiated gaseous exoplanets. Simultaneously, they have also shown that rotation can influence this transport, leading to highly irradiated, rapidly rotating objects that are uninflated. Here we explore the flows that underpin this transport, including the impact of synchronous or non-synchronous rotation. We used DYNAMICO to run a series of long timescale HD209458b-like atmospheric models at various rotation rates. For models that are tidally locked we considered rotation rates between $1/16^ th $ and $40$ times the rotation rate of HD209458b, whilst for non-synchronous models, we considered the range one-eighth to four times HD209458b. We find that our synchronous models fall into one of three Omega -dependent regimes. At low Omega , we find that the outer atmosphere dynamics are driven by a divergent day-night wind which drives weak vertical transport and can lead to the formation of a night-side hot-spot. At intermediate Omega , we find classical hot Jupiter dynamics, whilst at high Omega we find a strong Coriolis effect that suppresses off-equator dynamics, including the jet-driving standing waves, thus also reducing vertical transport. As for non-synchronicity, when small, we find that it has little effect on the dynamics. However as it grows, we find that temporal variations prevent the formation of the persistent structures that drive large-scale dynamics and transport. We find that rotation can significantly impact the atmospheric dynamics of irradiated exoplanets, including vertical enthalpy advection, which may help explain the scatter in the hot Jupiter radius-irradiation relation. We have also identified a seemingly robust atmospheric feature at slow rotation: a night-side hot-spot. As this may have important implications for both the phase curve and atmospheric chemistry, we suggest that this study be followed up with next-generation global circulation models (GCMs) that robustly model radiation and chemistry.