The lineup barely matters for gravity assist. Jupiter is the vast majority of the total you can get. Saturn has 30% of the mass and 2/3 the orbital velocity, so adding Saturn gets you only 20% more above using Jupiter alone (and the Voyagers didn't really try), and the ice giants are smaller and slower yet.
We could easily overtake Voyager via only Jupiter if we wanted to (and New Horizons eventually will), and Jupiter-to-any-target launch windows come at least every 12 years.
"The beauty of the gravity assist is that you use the gravity field of a large body to change course. A common misconception is that the gravity assist increases speed, but it actually leaves speed unchanged. It's more accurate to say that the gravity assist changes direction, since velocity is both a magnitude (speed) AND a direction."
That's only thinking about it from the perspective of the planet. Relative to the planet, the magnitude of the incoming velocity vector is equal to the magnitude of the outgoing velocity vector. But in the reference frame of the sun, the planet loses an infinitesimal bit of momentum, and the spacecraft gains that momentum.
And that's assuming you don't do an extra burn at periapsis, which is far more efficient at changing speed than doing the burn in interplanetary space.
Where is the quote from? Gravity exerts a force, therefore by newton's second law there is acceleration. Nothing says the acceleration is purely angular. The closer the pass to the planet, the greater the acceleration.
Wiki explains it well. From the frame of reference of ship and planet, the relative speed is the same. But relative to the sun, the ship can be moving faster.
"A gravity assist around a planet changes a spacecraft's velocity (relative to the Sun) by entering and leaving the gravitational sphere of influence of a planet. The sum of the kinetic energies of both bodies remains constant (see elastic collision). A slingshot maneuver can therefore be used to change the spaceship's trajectory and speed relative to the Sun"
There’s an upvoted sub comment to that which has a good correction. That statement as a whole is just not true and a meaningless statement. When you pass an orbiting body you will take some of that body’s orbital momentum and add that to your current momentum. There’s really no semantic argument in my mind that could justify the above statement. You change direction because you have more in total. There’s no bending of the direction here, just addition of new vectors but that’s exactly how all acceleration works anyway so it’s a bit meaningless to make that statement and I’m really not sure what they are trying to get at. Maybe from the pov of the orbiting body there’s no change but that’s not the thing anyone cares about when doing a flyby.
I think the issue mentally is if you treat the gravity of a planet like a valley, where you accelerate into it but on the way back out you lose all that gained velocity. The difference here is that the valley moves in the opposite direction ever so slightly as you pass it, and you gain the momentum from that valley's movement. At least, I think that's how it works.
[1]: https://space.stackexchange.com/a/3522
[2]: https://space.stackexchange.com/a/5076