A photo of the 'in progress' chewing would assist a little on this one. When you go to respond again, use the 'film strip' icon (middle of the features bar and follow the directions.
There is one outstanding thing that you did not mention and that is the needle. Even the best of needles can have a burr inside the eye which would do what you are describing.
The second issue would be that you take the newly rethreaded (but not yet in the needle) thread and use it as you would dental floss on your teeth. Gently draw it back and forth through the guides and watch for any snippets of thread that could be hiding there.
I hope that you have read and done the PE700 Instructions. It clearly shows where to cut thread and remove it when changing threads. Your machine is the next generation of the PE700 and the instructions are for ANY machine in general.
Another issue could be old thread. Sometimes when a dealer is selling a machine, they might throw in a dozen spools of thread that has a limited shelf life. Most threads are limited in their shelf life, but some last longer than others. IMHO Sulky is low on my list of recommend threads for these reasons. 1. Threads that are closer to the spool are usually more likely to be compressed and hold their 'tightly' wound condition. This is also true of the inside of the larger spools, especially in the metallic threads. 2. The configuration of the spool leaves more of the thread exposed to the drying of air (a natural event). 3. The light weight of the spool can hamper its ability to 'draw' the thread away from the spool making a slight increase in tension for even a moment. The excess tension can cause a small shred which eventually turns into a large shred and breakage.
Lastly, I have my own method of rejuvenating thread, you can see it here. This is my method and you need to decide if you want to try it or not.
You are really going got love machine embroidery when you get everything working right. Starting out can be frustrating, so read and ask a lot of questions. Post as many photos as you think will show your issue. AnnTheGran is the finest site on the Web for information - IMHO.
The dealer made embroidery look easy. It is when you know all the tricks and tips and especially your machine.
Pat, The Avid Embroiderer