In this paper, we consider a generalized space-air-ground integrated Internet-of-remote-things system with multiple unmanned aerial vehicles (UAVs) and low earth orbit satellites. To explore the diverse channel propagation conditions and adapt to the practical transmission environment, we investigate the three-dimensional node association among sensors, UAVs, and satellites, the spectrum partition between two-hop data collection links, and the multi-UAV deployment under the probabilistic ground-to-air channel model. Unlike existing works, we address the issue of user fairness by maximizing the minimum amount of collected data among all sensors. To cope with the formulated mixed-integer non-convex problem, we decompose it into two subproblems: a node association and spectrum partition subproblem, and a UAV deployment subproblem. To enhance optimized performance, the above two subproblems are solved alternately using the Lagrange dual decomposition and sequential quadratic programming. Simulations show that the proposed strategy converges within 15 iterations and yields an efficient solution, incurring an average loss of approximately 0.2 percent compared to the result of a brute-force search-based algorithm. Additionally, it outperforms benchmarks based on variable relaxation, successive convex approximation, and deep reinforcement learning under various parameter settings.