What if you didn't carry the fuel? Use stationary lasers from your starting point to power your journey half way until you lasers from your destination to slow your craft down.
I think the lasers would also need ~10,000 years of fuel, as opposed to ~10 years of fuel if you could somehow figure out how to carry it. But the energy to sustain in either case is probably measured in Dyson spheres, or some fraction of all energy in the universe pretty quickly too.
I could see the light spacecraft with their matter-antimatter engines laying down "lightways", like railroads in the old west. Once a lightway is established, then it's much less of a big deal to get from system to system. Apart from the tens of thousands of years in subjective time, of course.