The problem with picking up reaction mass along the way is, you need to lose energy to accelerate it up to your own current speed first before you can consume it as reaction mass to speed yourself up. As you get closer to lightspeed, even with perfect, lossless conversion, e.g. at 0.9c you lose 90% of the energy of the reaction mass bringing it up to your own velocity and get only 10% of it for beneficial thrust. The total of required reaction mass, which was already ludicrously huge for any practical payload, balloons massively.
If you do actualy have energy conversion losses, those limit your maximum possible speed. If you lose e.g. 1% of the energy you convert, then once you're at 99% lightspeed, the energy you gain from burning the reaction mass is the same as the energy you expended bringing it upto your own velocity. So there's no net gain.
A top speed of 0.99C only gives you a time dilation factor of about x2.3 or so.
And of course all of that is assuming magic fantasy tech with unbelievably high efficiencies and negligibly sized engines and mass storage.
Or alternatively instead of placing stationary fuel pellets in your flight path, have them accelerated by an external accelerator to as high a speed as possible.
You'd need to convert approximately 100,000x the mass of your capsule to energy to reach that kind of velocity, and the same again to slow back down at the other end. So for a one way trip, the payload would be on the order of 1/1,000,000,000,000th of the mass of the ship.
For comparrison, that means a starship the size of a Saturn V would be able to deliver a 3 milligram payload. If you assume even very slight efficiency losses, the possible payload size collapses quickly. Remember, some of that payload would need to be taken up by the propulsion system.