That’s the really hard part. If it’s almost science fiction to accelerate to 0.12c, it’s certainly much more difficult to slow down. At that speed we’d travel and pass this small system in mere minutes.
The issue is that in the original architecture without breaking you burn 50k tonnes of fuel to get 1k tonnes of payload up to 12% lightspeed. If you want to break all the way back to zero, you need to 50k tonnes of fuel to break. But that means you need to accelerate another 50k tonnes of fuel up to speed.
Which means you need 50 times for fuel to get from 0.11c to 0.12c, and you need to accelerate that fuel to 0.11c, so you need more than 50 times the fuel for the step from 0.10c to 0.11c, and an even larger factor more to accelerate from 0.09c to 0.10c, etc. So you don't just require another 50*50k = 2M tonnes of fuel, but an exponentially larger amount. The tyranny of the rocket equation