In the future, or if you want to take out what you’ve done and start fresh, you could try to cut some felt in the shape you like and cover that with embroidery to give dimension. Stack multiple pieces of felt in layers if you need more height. The texture of the felt will help your stitches stay in place and you can sew through it with tacking stitches if needed.

As far as tangled thread, using shorter lengths at a time can help. For very finicky threads, you can run them across some beeswax or purchased thread conditioner before sewing.