If the machine sews, I do not think the timing is off. Usually when the timing is off, you cannot even make a stitch.
The tension issue sounds as if there is some dirt or lint caught in the upper tensioning mechanism. If you have some ***unwaxed*** dental floss on hand, you can do this: lift up the presser foot to release tension, then see-saw the unwaxed dental floss back and forth to clean between the tension disks.
There is no point in paying $179 to re-time a $200 Singer 160. This is the new "featherweight" repro machine that came out a year or two ago, isn't it? Once it's broken, I would simply replace with a Brother from Walmart. It would probably be better quality. I wouldn't attempt to re-time a machine like this. I believe people who re-time machines at home are usually doing it on vintage Singers, not the newer ones.