The quilting thread may require a lighter tension than the Aurifil.
With the constantly breaking thread, I'd probably suspect the needle, first.
The thread should lie smoothly in the groove on the needle shank without a lot of extra room and without overstuffing the groove - and it should pass easily through the eye of the needle without squeezing it.
The groove protects the thread from abrasion as it's being pulled down into the fabric - and the same little section of thread may saw back and forth through the needle many times before it's deposited in the seam. :)
If the needle doesn't fit the thread to protect and guide it, you're going to have broken thread and needles and skipped stitches.
Try a size larger, then two sizes larger - or even the same size but in a large-eye type, like for top-stitching or metallics - and see if that doesn't help.
If you're already using a large needle and you've gone down to a finer thread, the eye may be too big, allowing the thread to whip around and catch on the point or otherwise tangle and break. Try a size smaller, then two sizes smaller.
I hope you can get it working well for you! :)