Cricket - just to be clear - you're not FMQing? The sponges I thought had been recommended for that, but I suppose there's no reason not to use them for help with other quilting too
As long as you're not pushing or pulling the fabric at a different rate than the machine wants, I can't see how it should be a problem.
What is your tension set at? How many layers are you going through when the thread snaps? I could see the glue causing a little breakage. When white glue dries in drops, the edges where we pierce it could be a little jagged... That might be why we hit it with an iron.
Vintage Singer needles are likely not a problem provided they don't have a burr in the eye or something but I do like topstitch needles because I find them more forgiving with that larger eye. Titanium is better wearing, I don't think it would make a lot of a difference in this case as far as thread breakage.
Is the thread shredding before it breaks, or snapping?
I'm sorry, I think I've just asked more questions than you did, but hopefully it will help us get to the bottom of it?