Conventional readout of a superconducting nanowire single-photon detector (SNSPD) sets an upper bound on the output voltage to be the product of the bias current and the load impedance, $I_mathrm{B}times Z_mathrm{load}$, where $Z_mathrm{load}$ is limited to 50 $Omega$ in standard r.f. electronics. Here, we break this limit by interfacing the 50 $Omega$ load and the SNSPD using an integrated superconducting transmission line taper. The taper is a transformer that effectively loads the SNSPD with high impedance without latching. It increases the amplitude of the detector output while preserving the fast rising edge. Using a taper with a starting width of 500 nm, we experimentally observed a 3.6$times$ higher pulse amplitude, 3.7$times$ faster slew rate, and 25.1 ps smaller timing jitter. The results match our numerical simulation, which incorporates both the hotspot dynamics in the SNSPD and the distributed nature in the transmission line taper. The taper studied here may become a useful tool to interface high-impedance superconducting nanowire devices to conventional low-impedance circuits.