Kirk,
I have encountered tool heads that were a bit tight, but it always turned out that there was a burr somewhere. Sometimes on the Key in the head, or in the keyway in the shaft, but usually around the hole where the taper pin is inserted. Try rolling a very fine file around the shaft in the area of the taper pin hole. If you see a bright spot it indicates a high spot caused by the taper pin being inserted too forcefully. Of course, I'm assuming your secondary head is a Star tool head. My experiance with Phelps tool heads is that they are more likely to be loose than tight.
You might also try running a jewlers file down along the key in the tool head, and along the the keyway in the shaft. We are not looking to remove metal, just locate burrs and remove if necessary.
Can you get the tool head on the shaft at all? If so, how far?