This might be the crucial mistake.
If a mass has:
25kg and 1m/s. Momentum = 25kgm/s
Then it turns around in a u-bend, it ends up with
25kg and -1m/s. Momentum = -25kgm/s

The momentum has reduced by 50kgm/s!!!! Not 25.

No , absoloutly not.
I notice you are dreaming again kallog.

but after it leaves the turn round it isnt accelerating !!
its free floating , thus your -25kgm/s is null and void.

and it is the acceleration of the masses that causes pipe momentum.

we are not decelerating the masses yet , other than the slight deceleration as the masses pass through the turnarounds , sure they reverse direction but they do not greatly decelerate.

therefore your -25kgm/s will not affect the motion of the pipe after it leaves the turnaround , because its not in contact with the pipe , and it does not press upon the pipe.

it would only affect the momentum of the pipe if the pipe
were applying a force to accelerate or decelerate it.

and lets not forget that the 2 masses at the ends cancel each other out , they will slightly slow down while passing through the turnarounds however ,and that -force could be used as a negative toward pipe momentum , but what you have posted is not valid according to newtons laws of motion.

so what you end up with is

1) a force is applied for 500 ft to a mass and that mass is accelerated to a given velocity.
2) when that mass reaches the turnaround and passes through the turnaround it will apply a force that would reduce pipe momentum , however that mass is not being stopped only decelerated slightly.

and then that mass free floats for 500 ft back to the other turnaround and passes through the turnaround and it will apply a force that would increase pipe momentum , however that mass is not being stopped only decelerated slightly.

the mass is then accelerated again for a distance of 500 ft

and you didnt mention that there is a constant acceleration of 20 masses as the above is occurring that provides for pipe movement.

Yep. If an object just turns around, then its moment becomes the negative of what it was before. Bounce a ball against a wall, and it's direction changes to negative, but its speed remains roughly the same. It's lost TWICE the momentum it had.

but the above would not apply to to pipe momentum , only the mass momentum , I thought that you understood that , I guess I was wrong because you seem to think otherwise or at least you would like for people to think that it would cause the pipe to not move , but as usual you are wrong again.
3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.