You’ve given numbers for how fast New Horizons launched, and for how fast Voyager 1 got thanks to the 1-in-175-years boost, but is there an easy way to actually compare them?

IE either what speed Voyager 1 launched at excluding the gravity assists, or what speed New Horizons would have reached if it were launched 175 years after Voyager 1 (to take advantage of the same gravity assists)?

Not easily. The tricky part is also in the relative numbers. The Voyager 1 data (and New Horizons data now) is in heliocentric velocity. The bit with NH being the fastest was with Earth centric velocity.

Another part in this is the "the probes are slowing down over time" - and you can see that with the Voyager 1 data that while the velocity after assist is higher than before, its not a line at slope 0 but rather a curve that is slowly going down.

This is further complicated because New Horizons had a launch mass of 478 kg and voyager was a twice as massive at 815 kg.

They also had different mission profiles (Could Voyager 2 taken a redirect from Neptune to Pluto? That trajectory change would have required a perigee inside the radius of Neptune...)

Voyager was done with a Titan III-Centaur rocket (that had a misfire) https://en.wikipedia.org/wiki/Titan_IIIE

> Voyager 1's launch almost failed because Titan's second stage shut down too early, leaving 1,200 pounds (540 kg) of propellant unburned. To compensate, the Centaur's on-board computers ordered a burn that was far longer than planned. At cutoff, the Centaur was only 3.4 seconds from propellant exhaustion. If the same failure had occurred during Voyager 2's launch a few weeks earlier, the Centaur would have run out of propellant before the probe reached the correct trajectory. Jupiter was in a more favorable position vis-à-vis Earth during the launch of Voyager 1 than during the launch of Voyager 2.

Note also in there that a few weeks difference between Voyager 1 and Voyager 2 had different delta V profiles (which is why Voyager 1 is faster)

New Horizons was done with an Atlas https://en.wikipedia.org/wiki/Atlas_V

... and I don't have enough KSP background to do the orbital mechanics for this.