I don’t think a stronger Remote ID system will work. Signal strength decreases as the square of distance for an omnidirectional antenna like a drone has. You would need a lot more power to make a significant improvement in distance and that means a much larger battery with more weight.
I think a better way is to use handheld radio frequency direction finding equipment to locate and jam a drone. There are a few of these devices on the market now like the NQ Defense ND-BD003 but they are expensive. I expect to see more of them on the market with lower prices given the proliferation of drone incursions and the publicity of incidents such as the drone hubbub in New Jersey.