It makes sense that the second one has a higher logp=-1.039... since it has lower standard deviation. The same way that a Normal distribution peak grows higher when you reduce the standard deviation.
If you really want the same logp at the peak when using different standard deviations I think you will have to derive a custom distribution that has a fixed height at zero and whose probability changes in the tails only (or do something funny with the degrees of freedom of the StudentT). This, however, would no longer be a StudentT, as far as I understand it.