My WA guess is that the collet ears got yielded - probably by tightening beyond its design range. To fix it half ass, it will need to be annealed, expanded till it yields the other way, and then rehardened. But it will likely lose some concentricity in that process. You could try just expanding it till it yields to just clear a 1/4 pin. But to be honest, I'm thinking it's probably toast. What does a new one cost?
Edit - I wrote this yesterday but forgot to press send. Sounds like you have done what I would have done. But reading your version, I think there might be a better way. Tightening on a taper probably won't correct a yielded collet where it needs to be corrected. Consider using the tapered mandrel to open the collet enough to allow entry and subsequent clamping of a series of calibrated pins each a few thou bigger than the one before it until a 1/4 pin will slide in without any interference at all. Sounds like you are already close, and maybe even "close enough", but the idea is to reverse the yielding at the former yielded location itself not elsewhere. This might make it useable but I'm not sure this will preserve the original concentricity of the collet. You will have to confirm that yourself. Worst case, you buy another 1/4" collet.
