Chris,
I ran into the same problem with some shoulder straps.
Kaleb's idea of hand advancing the machine to get it started worked for me. I had to push and shove and squeeze and press the layers under the presser foot. Once it was down and under pressure I could sew but I still needed to hand advance every now and then.
My layers at their thickest were:
1) Two layers of Quest Outfitters light weight nylon webbing
2) One layer of DP VX21 fabric
3) One layer of 1/2" CCF
4) One layer of 4mm Spacer Mesh
Two good things came out of this experience.
I got the straps sewn and finished. I also learned my machine's limit.
If I keep this up I'll soon be looking for a commercial machine with a presser foot that raises higher and a motor with more power!
What about a shoe repair shop or a leather craft shop for a stronger machine?
Good Luck!
Party On,
Newton