Starship Asterisk*

http://antwrp.gsfc.nasa.gov/apod/ap051022.html
Looking at the shape of this galaxy I would say the collision was NOT done by a small galaxy going through the centre but by the core of the galaxy shifting faster to one side maybe by push pull by another galaxy.
Most galaxies have gone through some form of collision. Even our own Milky Way look at our 3 little saterlite galaxies.

with a one on distance-squared relationship for the force exerted on objects by gravity it would seem to me that another galaxy would have to float very much straight through to have the center taper out as it does in that image
(i expect it is stretched in the direction of movement of the colliding galaxy)

Maybe - but a ripple on a pond moves perpendicular to the distrubance that caused it.

this is more of a gradual dragging effect

True - but if it passes through the middle, it'll initially be dragged on way, and then the other producing a more ripply type effect?

Something has changed the structure of a spiral galaxy.
If a smaller galaxy went through the centre there would have been a pulling effect causing a much deformed galaxy. This would have been over thousands of years. The shift of the galactic centre to the left with a deformed spiral would also require the loss of gravity from its centre.
Must think more on this line.
The shift must have been very slow but! quick caused by an external force affecting not only the galaxtic centre but also the structure of the spiral. Maybe a combination.
Hey! maybe a few large blackholes near the galactic centre created a chaos that may have ajusted the galactic centre.

Stay Cool