I would be careful about knocking out the key. Although your tool head has the 3/8" hole at the taper crimp station, it is actually what I consider to be a newer style tool head. Tool heads like yours have a pin through the side of the tool head that goes into the key. If you attempt to remove the key, you will really bugger it up. Even on the Old style tool heads that do not have the pin, you are likely to bugger up the key trying to remove it.
I have never seen a Star tool head where the key sticks out too far, although it often seems that might be the problem.
The most frequent problem is at the taper pin hole. If the pin is inserted with too much force, the it can deform the hole a bit and cause a raised area around the hole. Role a very fine file over the hole in the column, front and back, and see if you see a raised area. If you do see a raised area keep rolling the file over the area until the raised area is flush with the rest.
If the problem is not there, then there could be a burr in the keyway, or on the bottom of the key. Run a fine file along the inside edges of the keyway to see if you can find a burr. If you don't find anything there, try to file the corners of the key while it is still in the tool head.
Of course if none of that works, you can send it to me,
Bruce Williams