Battery-free sensor tags are devices that leverage backscatter techniques to communicate with standard IoT devices, thereby augmenting a network's sensing capabilities in a scalable way. For communicating, a sensor tag relies on an unmodulated carrier provided by a neighboring IoT device, with a schedule coordinating this provisioning across the network. Carrier scheduling--computing schedules to interrogate all sensor tags while minimizing energy, spectrum utilization, and latency--is an NP-Hard optimization problem. Recent work introduces learning-based schedulers that achieve resource savings over a carefully-crafted heuristic, generalizing to networks of up to 60 nodes. However, we find that their advantage diminishes in networks with hundreds of nodes, and degrades further in larger setups. This paper introduces RobustGANTT, a GNN-based scheduler that improves generalization (without re-training) to networks up to 1000 nodes (100x training topology sizes). RobustGANTT not only achieves better and more consistent generalization, but also computes schedules requiring up to 2x less resources than existing systems. Our scheduler exhibits average runtimes of hundreds of milliseconds, allowing it to react fast to changing network conditions. Our work not only improves resource utilization in large-scale backscatter networks, but also offers valuable insights in learning-based scheduling.