> current vehicles traveling about 10x the speed of voyager
As I understand it, not really. Parker Solar Probe is crazy fast, but only because it has that trajectory, and is unable to just change course and keep that speed in other directions.
If you want to launch something for deep space, the Jupiter-Saturn slingshot is still the most powerful trajectory we know of.
Today's rocket engines would give the probe a higher initial speed, but the final velocity would not differ dramatically. A fair bit higher, but not orders of magnitude.
You can do a Sun-diving Oberth maneuver too. Project Lyra was a proposal for an `Oumuamua flyby that got over 50km/s: http://orbitsimulator.com/BA/lyra.gif