Arctic regions, such as northern Canada, face significant challenges in achieving consistent connectivity and low-latency computing services due to the sparse coverage of Low Earth Orbit (LEO) satellites. To enhance service reliability in remote areas, this paper proposes a hybrid satellite architecture for task offloading that combines Medium Earth Orbit (MEO) and LEO satellites. We develop an optimization framework to maximize task offloading admission rate while balancing the energy consumption and delay requirements. Accounting for satellite visibility and limited computing resources, our approach integrates dynamic path selection with frequency and computational resource allocation. Because the formulated problem is NP-hard, we reformulate it into a mixed-integer convex form using disjunctive constraints and convex relaxation techniques, enabling efficient use of off-the-shelf optimization solvers. Simulation results show that, compared to a standalone LEO network, the proposed hybrid LEO-MEO architecture improves the task admission rate by 15\% and reduces the average delay by 12\%. These findings highlight the architecture's potential to enhance connectivity and user experience in remote Arctic areas.