Looks like you made the edge even faster than in the previous version!

Thank you for posting the results. I've seen something similar with a 7414 in a video from W2AEW, where he's using all the remaining gates to drive the output.
https://youtu.be/9cP6w2odGUcSeen that video some time ago, and for some reason I was under the impression that he used only one resistor, and that's why I was insisting for only one resistor. Now I see he used a resistor for each gate. Not sure where I've seen the 7414 gates in parallel and a single resistor, or if that was just a test idea that came while watching his video years ago.

Maybe it was something that I only assumed it will work better, or maybe I've seen it in some other schematic, I can't tell. Writing these because, now I'm puzzled. Why did he used a resistor for each gate? Maybe there is something that I'm missing. Maybe a resistor for each gate makes the edge even faster, or maybe it doesn't matter, I don't know. The thing is, now I'm not that sure about my reasoning with the series parasitic inductance for each R.

Anyway, back to your current results, it looks like you may need a faster oscilloscope, or a similar bandwidth scope but analog, not digital.
Saying this because of the small bump
before the raising edge. That is usually a digital artifact, because of the sin x/x interpolation. If it is possible to disable the sinx/x interpolation, try to see if that bump before the raising edge disappears. The signal doesn't "know" in advance when the next edge will come, so it can not "ring" before the edge. Ringing can happen only
after an edge has occurred, not before.
That bump before the edge might also be a reflected signal from the previous pulse, but I doubt. Can be tested by changing the frequency of the pulses, and see if the ringing before the edge moves in another position, or disappears. Or, by switching to dots mode display while turning off the sin(x)/x interpolation, and observe if the preceding bump disappears.
What I'm trying to say is, the exact value of the raising time might be slightly different than 960ps (if measured with a high bandwidth analog oscilloscope), because the digital oscilloscope tries to reconstruct the edge from very few samples, 7-8 samples for 1ns at 8GSa/s. While doing so, the oscilloscope assumes the bandwidth of the signal is limited to the datasheet specs, while in any fast edge signal there is still a ton of harmonics at frequencies above the oscilloscope specs, and such the fake ringing before the edge (produced by the digital post-processing of the samples, post-processing that is done to turn those very few samples into a continuous trace on the screen).