You can smooth out the flat-top by adding a little series R from the emitter to the output cable connection. This will trade some edge speed for more civilized appearance afterward. Remember, nothing is really impedance matched here, so trade-offs need to be made, depending on what features are needed. If the goal is to get more flatness and pulse width for viewing lower speed scope performance, the rise time and amplitude are probably plenty good enough already, so you can give some up. I didn't notice in the discussion anything about provision for pulse extension, just that there's about 6 nSec of 141 line inside. Do you have the open end of the charge line going to an SMA connector for external line? That would take care of pulse width, so cleaning up the waveform is next. I'd recommend trying a small SMD series R, like from a few ohms up to maybe 22 ohms, experimentally.
Also note that there is such a thing as too fast a rise time when checking lower speed equipment. When checking scopes that are native 50 ohm input, it should be good to go, but for setups with 1 meg inputs with an added termination, there will be a number of discontinuities and reflections - the scope is mostly a capacitive load, and a very short test signal rise time will aggravate the situation. This can make it difficult to assess the response to "normal" signals the scope would encounter, although it would show what it actually does at very fast edge speeds.
Ed