We present an improved dynamical slab ocean model implemented in a 3-D General Circulation Model (GCM) called the Generic Planetary Climate Model (Generic-PCM; formerly the LMD-Generic GCM). Earlier two-layer slab ocean models featured wind-driven Ekman transport, horizontal diffusion and convective adjustment. Building upon this, our updated parallelised model introduces a Sverdrup balance scheme for Ekman transport, the first application of the Gent–McWilliams (GM) parameterisation of mesoscale eddies in a slab ocean model, and a spectrally and thickness dependent formulation of sea ice and snow albedo. We validate this model in an idealised aquaplanet setting under various OHT configurations. We show that enabling OHT transforms not only surface features – such as cooler tropical sea surface temperatures (SSTs) and reduced sea ice coverage – but also atmospheric structures, notably producing a double-banded precipitation pattern across the equator driven by Ekman-induced upwelling. Our modelled meridional OHT profiles show first-order agreement with fully coupled atmosphere-ocean GCMs, with Ekman transport dominating in the tropics (enhanced by GM-induced restratification), and diffusive plus GM contributions peaking near the ice edge. When applied to modern Earth, the OHT-enabled configuration yields an annual global average surface temperature of 13 °C, within 1 °C of reanalysis estimates, and improves extrapolar SSTs and sea ice coverage relative to the OHT-disabled baseline. Seasonal SST and sea ice biases relative to observations are also significantly reduced to within 0.6 °C and 3 million km2, respectively. We obtain a planetary bond albedo of around 0.32, in close agreement with observations. Together, the aquaplanet and modern Earth benchmarks demonstrate that our developments represent a clear improvement over earlier two-layer implementations. We further show that GM-induced restratification reduces the need for explicit convective adjustment, while also strengthening Ekman transport. In addition to improving equatorial dynamics, the inclusion of the Sverdrup balance also reduces hemispheric asymmetries. Notably, due to model parallelisation, these improvements are achieved at almost no additional computational cost compared to OHT-disabled simulations run over the same number of model years. This enables long integrations and large ensemble studies, making the model particularly well suited for exoplanet and paleoclimate studies where broad parameter exploration is essential.