However Anything orbiting the sun wouldn’t be able to stay on target to fire the fuel for long. Calculating the trajectory to account for gravity would be problematic. The whole process would be too brittle, if something went wrong it could well be impossible to recover.
Nifty idea was to fire the pellets before and after, so when it flips mid-flight it could collect fuel pellets to decelerate.
Couldn't you just make every fuel pellet a powered spacecraft just a tiny engine? It could adjust its velocity when it drifts off course. That would add some weight, but a small ion engine might fit the bill. The engine could of course be disposed of to save weight once its captured by the larger ship.
The whole process could be safer if the rocket just keeps some extra fuel in case it doesn't manage to collect say every 10th pellet.
But if the pellet track is moved off target you have to follow it.
By the way I like to call it the PacMan Rocket.
Hint: Make sure the reaction mass misses the rocket ship.
I picture it like this: There's, say, a one degree angle between the trajectory of the ship and the trajectory of the fuel pallet. The explosion can happen arbitrarily far before their courses intersect. This means that the blast can be (arbitrarily far) * (sin 1 degree) away from the course of the rocket.
But that [Edit: the fuel pallet] transfers a small amount of sideways momentum to the rocket. To counter that, alternate fuel pallets from the left and the right.