Applying external magnetic or electric fields, especially via a Riga plate, significantly improves flow efficiency by reducing friction and turbulence, enabling better flow management. This enhancement is particularly advantageous in enhancing the performance of engineered systems and turbomachinery. Consequently, our research delves into the dynamics of a low-ionization fluid in an extended infinite porous Riga channel within a rotating setup influenced by Hall and ion-slip electromotive forces. The model examines various pressure gradient scenarios: impulsive pressure gradient (IPG), cosine pressure gradient (CPG), and sine pressure gradient (SPG). We represent this flow model through time-varying partial differential equations and solve these using the Laplace transform (LT) method to obtain exact analytical solutions. Our research carefully delineates the dominance of key factors on the flow traits, employing graphical representations for IPG, CPG, and SPG scenarios. Our key observations reveal an amelioration in the modified Hartmann number notedly enhances the velocity components for all pressure gradient types. A higher rotation parameter tends to reduce the primary velocity's shape profile, while the secondary velocity exhibits the opposite trend. The primary velocity notably boosts with a rise in the Hall parameter, whereas the secondary velocity decreases. Both primary and secondary velocities are generally higher in the IPG scenario than in CPG and SPG. Additionally, a greater modified Hartmann number intensifies shear stresses in all pressure gradient cases, with the shear stresses at the lower plate being lower in IPG than in CPG and SPG. These findings offer substantial contributions to various sectors, including nuclear reactor technology, spacecraft propulsion, satellite operations, space exploration, aerospace engineering, and so forth.