Yeah, Voyager 1 was launched on a Titan IIIE. I don't really want to do the delta v calculations, but if we look at mass to LEO as a rough proxy, Titan IIIE does 15,400 kg and the Falcon Heavy does around 50,000 kg (with re-use). New Glenn can apparently do 45,000 kg. Doesn't take into account gravity assists, but 3x the capacity before Falcon Superheavy or refueling gives us a helluva lot of leeway.

Its not "interstellar speeds" but I'm pretty sure we could get probes further out than Voyager 1 faster if we put the money behind it.