I'm pretty sure your 1/4" fittings are the slowdown - I watched the video, and it gets slow when the largest section of the 2-stage ram is collapsing - this is because you have a LOT more fluid to displace in the larger of the two stages than in the smaller one.
This is also one of the benefits of a multi-stage cylinder for a dump - you have the greatest "push" where it's the hardest to get started, when the push points and cylinder are nearly in line. As the cylinder raises, your geometry changes and requires less push to keep moving. My 6-yard dump truck has dual 2-stage cylinders, and I can't put enough heavy or wet stuff in that thing to slow it down :=)
If you decide it matters, I'd upsize the smallest fittings/hoses in your system and see what happens. But you're right, the smallest diameter in the system will dictate the speed, so everything would need to be the larger size in order to see much (if any) change.
Keep in mind that a cylinder with 1.4 times the diameter of another cylinder, will require TWICE the flow to move the same distance. (Area of a circle is the formula) -
Sooo, from the cylinder's viewpoint you need to move a LOT more oil to move the larger section of the 2-stage the same distance -
but the good news is, from the FITTING/HOSE point of view, the same formula applies - so if your smallest fitting is 1/4" and you go to 1/2", you will increase the flow by 4 TIMES. Just going from 1/4 to 3/8 will DOUBLE the speed that last half of the dump cylinder moves, assuming all other variables remain the same... Steve