My mother and I both were having the same looping on the back problem on an intermittent basis with our new Kenmore machines. I did a search on the internet and found a site that said to be sure you thread your machine with the presser foot up. If you thread with the presser foot down, the thread does not seat in between the tension disks properly. Once we started doing this, we have not had the problem again (except when I forgot to put the presser foot down).
With that being said, I have an old Singer machine I bought in 1984. It wouldn't drop the feed dogs, but had a cover. I understand your problem with the cover in place because it was very difficult to move the quilt sandwich around on it as well. I found I could do better by not covering the feed dogs. With the hopping motion of the darning foot, I was able to move the quilt without interference from the feed dogs. It was not an ideal situation, but the only way I could use the machine for quilting.
I bought the new Kenmore machine when my old Singer finally quit and I love it. It will drop the feed dogs and has the needle up/down feature I was looking for.
I hope you get your machine working properly.