You are moving at 0.25c relative to the buoy and the buoy is moving at 0.25c relative to the Earth, and to get the correct value for your speed relative to the Earth, you must use the Relativistic velocity addition formula. Thus the correct answer is

= 0.47c.

If you drop a second buoy and then accelerate for another 90 days, you will now be moving at

= 0.64c relative to the Earth.

After another 89 days of acceleration, you will be moving at 0.77c

So in the first 90 days, you changed your speed relative to the Earth by 0.25c

In the second 90 days you changed it by 0.22c

In the third 90 days you changed it by 0.13c

In a fourth 90 days it will only change by 0.085c

In a fifth, 0.055 c

Etc.

Note how each 90 days of acceleration gains you a smaller and smaller gain in speed relative to the Earth.

So, after 450 days of acceleration, you will be moving at 0.91c relative to your initial "rest" speed. Even if you had been moving at 0.91c this entire time, you will have only moved 1.12 ly by your reckoning. The length contraction at 0.91c is 0.415. So according to the Earth frame, you will have moved 2.7 ly. (However, since you were not traveling at 0.91c for the entire time, you will have actually moved less.)

Ergo, in 450 days of your own time, you could not have traveled to even the nearest star.