Just to confirm, on the back of the CJ 60, you have two roller bars that you can set your media on?
One nice thing with flanges on the media roll and using them is that when you load the media, you can get it started through the front a foot or so and then roll the media roll backward to snug up the media while holding the center of the media slightly in the front to create tension. This helps straighten it right off the roll. From there you lower the rollers. Also with the flanges you would have the two collars that sit on either side of the flanges (over one bar) to keep them from wandering. I think you would notice much better feed and much straighter.
Seems when you set media right on those roller bars the weight of the media makes it hard to track straight.
If you can set a piece of media that you know is cut straight into the printer and line up with the front edge of the cutting strip or platten (using outside rollers only) , then move the media back and forth several times. If it comes back still perfectly lined up with the same line you lined it up to start with, the rollers are still good.
I would say find some flanges first. May be an easier fix than the rollers.