Some time ago I read a theory stating that in a long past Jupiter may have forced Saturn in larger and larger orbits , which in his turn moved  Neptune in even more larger and more eccentric orbits .  
Neptune may have this way attracted bodies out of the Kuiper belt - and even Pluto -  
Parts of them can have build part of the asteroid belt ...
The main force doing this job is called resonance resulting in migration .  
Googling for resonance gives a lot of information .  
The attracted asteroids may have caused the big lunar bombardment some 800 miljon years ago .  
In order to find out some trends I simulated the solar system back in time for about 800.000 years , using the Picard integrator .  
The result is shown herunder in the picture .  
The results for the SMA were omitted ( they show a lot of "noise" ) but interesting is the strong resonance between Jupiter and Saturn . Their eccentricities and inclination are inversely bound . When Jupiter is far or high ,Saturn is short or low and vice versa.  
Some resonances can also be seen for Uranus and Neptune , both influenced by a combination of Saturns and Jupiters movements .  
In this short time scale it is not clear that Neptune may evolve to large eccentricities ...  

This might be of interest to you.  Last year I gave a presentation to my Astronomy class about the Resonant Capture Theory.  Here is my powerpoint presentation:
http://orbitsimulator.com/astro490/final.ppt
 
You can planetary migration in the beta version of Gravity Simulator using the Autopilot's "Continuous Orientation" and "Thrust" commands.
 
If you start Pluto in a circular orbit beyond Neptune, then make Neptune migrate outward, as its 3:2 resonance (or any strong resonance) sweeps past Pluto, it gets caught in the resonance and migrates out with Neptune.  The further it migrates, the more elliptical its orbit becomes.

Heres the same simulation as above , run for 9000 years , viewed edge-on, but at on angle of 90° from the previous one . Screen scale is also 100 AU . Neptune is shown here at the right .

Your last animation is similar to one on the "Simulations" page of this web site:
http://www.orbitsimulator.com/gravity/articles/pluto.html

There is no resonance with Uranus.  You're seeing the elliptical shape of its orbit in the rotating frame, but unlike Pluto, it marches forward indefinately in the same direction, rather than slowing to a stop and reversing periodically.  Hence, no resonance.