In short: to have any sort of survivable encounter with the object the relative velocities need to be so small you have essentially "matched their speed". Those last 0.5 km/s you might gain aren't important compared with the 29.5 km/s you need to put in.
you don't match deltav, you'd match trajectory. you may be able to do that at the cost of more or less deltav, depending on how clever and patient you are. once you've matched trajectory, you'll (basically) stay matched, as you're in space and there's nothing to disturb you.
Elsewhere I saw what I thought was the speed of the comet, which was around 69k mph. Didn’t Helios 1 and 2 do something like ~150k mph?
Assuming those numbers are correct (please say so if not), then what would stop an intercept from being technically possible (even if very very very hard)?
To actually hitch a ride with another object you have to match their velocity _and_ their location at the same time.
If the object you are trying to catch started further from the sun than you, and was already moving faster than you, then you can't match its speed and location by falling toward the sun: when you arrive at the same location, it will have fallen further than you and hence picked up more kinetic energy per unit mass than you did, and it started off moving faster than you to start with, so it's still moving faster.
That remark makes more sense in the context of missile defence than when talking about space travel.
From what I know from reading on Helios-A and Helios-B, we already have a probe which can go over twice the speed of what I thought I saw the comet is traveling at. So couldn’t the probe match its velocity (dunno why I said Delta V before) to the comet, if even just for long enough to land without total destruction?
And if you don't match it well enough that you end up roughly the same place you're going to have a fast, and therefore violent, encounter.
Dunno why I said DeltaV, but clearly it was inappropriate.
Yeah, but we could go to other stars already, in like a zillion years. Voyager is on an interstellar path, although it isn't pointed at a nearby star. If the object has made the journey it might take the same delta-V for us as an interstellar trip, but it would happen a whole lot faster.