To reinforce Cash's Mom post, sometimes it is the thread itself and not the cone or whatever.
If you return everything back to normal and put in a different thread, (strong suggestion: time for a test sandwich of the same batting, and similar backing/top fabrics) is it better? Sometimes it is a clear answer that, yeah, it was the thread all along and nothing you are going to do is likely to make it any better. If you absolutely positively have to use that thread, try a couple more things. First off, is it worse on one side or the other, or what do you see as the issue for the skips. Then try reversing the direction of the thread. So if you think it is what is coming off the cone, take another bobbin and thread and use that as your top spool. If you think it is the bobbin, rewind a bobbin onto a fresh bobbin. Label everything and see if there is a combination that is better.
If not we have to look at other issues, whether that is needle size, type, etc. Or maybe a machine issue, most likely just an adjustment (or sometimes a good bobbin case area cleaning can clear up any number of issues).
By any chance is your thread black or at least a dark color? I've been told that black thread is often over-runs or bad colors from other dye lots and have been worked and reworked and dyed several times. So I don't know if it is just a self fulfilling prophecy, but I do seem to have a lot more problems with bad thread the darker it is...
You didn't mention a long arm and so I'm assuming a domestic machine and that there are no encoders or anything that need cleaning. Are you using any sort of special feet, or something like my BSR (bernina stitch regulator) that might have a tiny laser or sensor?