using a router/table a jointer

Check your fences and table for flatness. Your shim may be causing a problem. I doubt a bit (even a bad one) would cause a teeter-totter.

Are you maintaining consistent contact with the oufeed side of the fence once enough stock is in contact with it? Assuming everything is straight & flat as it should be, once enough stock is contacting the outfeed side of the fence, you should not be using the infeed side to guide the stock. Is it possible that the teeter-totter you speak of is just some snipe at the beginning or end of the cut? If so, it may be unavoidable but you can compensate by using longer stock than the finished size and cutting to length later.

All that said, though, I would recommend that if you have a halfway decent tablesaw, you look into one of the methods used for jointing an edge on the saw. I use a carrier-board and with a good blade can make a glue-joint quality cut very quickly, perhaps at the most requiring a pass or 2 with a jointer plane but usually that is not necessary.

In addition to all of the other things that have been suggested... is your stock flat? If the face of your stock won't lay flat on the surface of your router table, you're never going to get a good edge jointed on it.