Have you manually operated the machine backwards to see if you can tell when it hangs up? Take off the cover plate so you can see the action of the bobbin and bobbin case and the needle as you turn the wheel. Could the bobbin case have gotten bent? Do you have all parts of the broken needle? Could there be a stuck piece that only hangs it up in reverse?
I'm not sure but if you can sew forward but not backwards wouldn't this mean it isn't a timing problem. If the timing was off wouldn't it not work in either direction?
Also could a local sewing machine repairman possibly do something? I've heard that longarms aren't that different from regular sewing machines and local repair people can work with them.
Good luck. I hope you figure it out before it has to go somewhere.