Hi [Whatever your name is],
If the timing is only off by half a tooth: Have you tried loosening the grub screws in the hook-driving gear, tapping it slightly to the left or the right to compensate, then tightening the screws back up? As long as the teeth still catch you're in business.
One other thing to check: Open the slide plate so you can see the hook, then jiggle the handwheel back and forth, the absolute minimum amount you need to get the needlebar to move up and down. Now look at the hook and see if it responds to even the tiniest jiggles of the handwheel. When I did this with a well-used 111w155 I picked up, I observed that while the needlebar moved even if I rotated the handwheel a millimeter, it took several millimeters of handwheel movement before the hook responded. In other words, the hook gear was worn out and had enough slop that it was affecting the timing.
I ordered a replacement hook gear and corresponding hook-driving gear online, but the damned things were made overseas and had less than fine tolerances. I had to take the hook gear to a machine shop and get them to shave a couple thousandths of an inch off of the top of it to get it to fit between the bearings. Even then, if I meshed the gears up snugly they'd start to grind once a rotation, as the teeth are not 100% consistent. I had to compensate by tapping the hook-driving gear quite far to the left, but not so far that the teeth don't grab, and finally managed to get the timing right with some back and forth.
hope that helps,
- Nick
Vintage Singer Sewing Machine Blog
http://vssmb.blogspot.com/