[myrmidon]

If you circularize the orbit at 550 AU (which is costly but possible, at ~1km/s of delta-v), then you end up with an orbital period of >10000 years (to complete your whole-sky survey in one plane).

But first-- the price to get that circular orbit is steep, you end up imaging empty space for a lot of the time (no real way to "skip ahead") and your orbital speed vector makes you leave the observation cone for any interesting target pretty quickly.

In conclusion: You probably really want to stick with "one telescope probe per target system", and to give them one-shot orbits because those are cheap, reasonably fast and inside the observation cone (for your single target) for longer.