If you read that website and others that discuss Orbital Variance, they have measured changes in the earth's orbital length with atomic clocks. The year is getting longer right now as we also experience warming.
As for why the earth does not follow a perfectly elliptical orbit (or circular) here is a practical reason... when a body is travelling in free space and encounters the gravitational pull of another body, it will (if captured) begin to orbit that body with either an elliptical or circular (both are equivalent with the circle being an ellipse with a single locus) orbit.
Now, over time, the orbiting body will assume a constant orbit if there are no other elements in the equation. However, if there are other bodies with gravitational effects on that body, depending on their orbits and positions at any particular time, they can create shifting effects on that body.
I would speculate that the "alignment of the planets" occurs due to the mixing of their orbital frequencies creating nodes where they combine and cancel their impacts on earth's orbit, thus changing it slightly.
Note, the page I linked shows relationship between the shape of the orbit and global temperatures. Long before human CO2 production began.
If there are other bodies with such a large effect it would be easy to run numerical simulations. The main body, aside from the sun, that has an effect on earth's motion is the moon. As the moon leaves earth, earth's orbit would be affected, but this is not a repeating event. The main motion that has not been satisfactorily explained is the precession of the equinoxes and calling it 'wobble' is probably overlooking an obvious cause.