We calculate the kaon-interferometry radius parameters for high-energy heavy-ion collisions, assuming a first-order phase transition from a thermalized quark-gluon plasma (QGP) to a gas of hadrons. At high transverse momenta K(T) approximately 1 GeV/c direct emission from the phase boundary becomes important; the emission duration signal, i.e., the R(out)/R(side) ratio, and its sensitivity to T(c) (and thus to the latent heat) are enlarged. The QGP+hadronic rescattering transport model calculations do not yield unusually large radii (R(i) < or = 9 fm). Finite-momentum-resolution effects have a strong impact on the extracted interferometry parameters ( R(i) and lambda), as well as on the ratio R(out)/R(side).