We consider transporting a heavy payload that is attached to multiple multirotors. The current state-of-the-art controllers either do not avoid inter-robot collision at all, leading to crashes when tasked with carrying payloads that are small in size compared to the cable lengths, or use computational demanding nonlinear optimization. We propose an efficient optimization-based cable force allocation for a geometric payload transport controller to effectively avoid such collisions, while retaining the stability properties of the geometric controller. Our approach introduces a cascade of carefully designed quadratic programs that can be solved efficiently on highly constrained embedded flight controllers. We show that our approach exceeds the state-of-the-art controllers in terms of scalability by at least an order of magnitude for up to 10 robots. We demonstrate our method on challenging scenarios with up to three small multirotors with various payloads and cable lengths, where our controller runs in realtime directly on a microcontroller on the robots.