. . . which would seem to argue for getting a telescope into deep space to get some serious parallax. Possibly a Pluto-type solar orbit?
No, that would not be useful. Most Earth-crossing asteroids are going to have orbits that are comparable to Earth's orbit, so the baseline you really need is much smaller than that. Further, you'd need one amazing telescope--a super-Hubble--to spot something so faint from that far out, and you sure can't service it out there. And finally, it would take many years to get such a device into such an orbit, assuming you had the capability to launch such an monster out there.