The boat is probably 15 to 20 years old. The previous owner said it had been stored for 12 years. The jib is in worse shape than the main, probably from UV damage on the furl.
I measured sailing angle by tacking to round a buoy. I would sail close hauled until I figured I could round the bouy on the other tack. I had to let the buoy come around to the 4:30 position (135 degrees off the bow) before I was successful. The angle to the true wind is half that. If I tacked with the buoy at the 3:00 or 4:00 position, I would have to tack again to make the mark.
I have played with the rake a little. The Hobie U document recommended against rake for the 18. This makes sense to me because the 18 has daggerboards. By raking the Hobie 16 mast back, more of the hydrodynamic lift is generated by the rudders and less by the hulls. Since the rudders have a higher aspect ratio, they can generate lift with less induced drag, which helps pointing. With the 18, you want the daggerboards generating the hydrodynamic lift.
Does rake help with your Tiger?
I always found a bit of rake helped my 18's. Don't go overboard but a bit helped our pointing ability. It sounds like your jib is well past it's used by date as probably your main. Some new rags would definatly help. How much mainsheet tension do you have?
Also - the only way to accuratly measure your tacking angle is to get a compass and go from tack to tack.
The Tiger is a very different boat to the 18. We do tip the mast back a bit but the settings are totally different to the 18.