I found them

 See how small this box of 100 needles is?  No wonder I couldn't find them!

They were in this tray of other sewing stuff in a box of fabric, under the quilting machine.  I must have put it there temporarily when I needed the room on the quilting frame for a big quilt.  Then, the box got moved and more fabric got piled on top of the tray.  Totally logical, but oh, so frustrating.

I've changed the needle and now the quilt goes 24 inches before the thread breaks.  Progress!

This quilt is just going to take a lot of babysitting today to get done.  That's ok because I have a lot of work to get done in the quilting room.  More fabric to sort through and cut.  Sounds like the thread broke again.   I was really hoping the needle would fix the problem completely and I could get this quilt done quickly.  Oh, well.  It will look good when it does finally get done and next time I WILL change out the backing fabric for something that my machine does like better.  I know other machines are ok with that backing fabric because I was on the Facebook page of one of the local quilt shops and saw a very similar quilt on one of their machines being quilted.  They didn't complain about the quilt or having troubles.  Of course, they have a $30,000 machine too which can quilt through practically anything :)