The layering issue you are describing, where the stitches get wonky or you get those little loops underneath, is almost always related to fabric feeding, especially with denim. The machine is trying to pull through multiple layers of heavy material at once, and if the top layer moves independently of the bottom layers, you get distortion. A walking foot definitely makes a difference here; it helps pull all layers through evenly, which should drastically reduce those thick spot problems. It's a tool for when you're dealing with multiple, dense fabrics, so it's probably a good investment if you do a lot of outerwear.
Regarding the thread, if your chunky specialty thread is skipping, it could be that the thread is simply too thick for your machine to handle consistently, even if it looks great. Machine threads are designed to have a specific weight and diameter. Try running a few test seams with a heavy duty polyester thread that is specifically marketed for denim, but maybe one that is slightly less massive than the specialty contrast thread you bought. You might find that a standard heavy-duty thread behaves much more predictably, even if the contrast isn't quite as aggressive as you want.
If you want that strong, visible contrast, I'd suggest trying to adjust the tension settings on your machine rather than switching thread types entirely. Sometimes, if the top thread tension is just a hair off, it pulls unevenly across those dense seams, which can make it look like the thread is skipping. Since you mentioned you tried going slower, keep doing that, but also make sure your needle is sharp and appropriate for thick denim. A dull needle can create friction that throws off the tension, especially when stitching over a seam allowance. Also, when dealing with denim layering, sometimes slightly shortening your stitch length below what you think is necessary actually helps stabilize the seam, even if it feels counterintuitive to what you tried before. It gives the machine less distance to travel and helps the fabric hold itself togather better through the thick areas. It's just another thing to try if the feeding issue persists.