Yes, the strap goes all the way around. That's why I think the given 50inches in the pattern might be too little - the bag is quite above the hips now and not really suited to put around the head, just around the shoulder. If I ever were to make this again, I'd definitely go for a longer strap.
As for the sewing machine, dusting might do you more good if you want to prevent it from smoking. Oiling it might be a good idea for the overal performance though
I hope to upload the "finished" pictures tonight.