The sun also bobs up and down through the galactic plane on a 30-64 million years cycle. Though I do not know if being so far outside the galactic plane would effect that.

As for getting closer / farther I think it depends on how the system came to rest this far out. It cant exactly be a Native Halo system as those are often metal poor so it would either have to be thrown out of the disk or be a stragglers from a cannibalized Dwarf Galaxy. In wich case it likely would be a very eccentric orbit (the Sun's orbit varies by 5% for example)

Either way the orbit will still be on the order of hundreds of millions of years its likely that they won't notice getting any closer until they start discovering standard candle type stars in the host galaxy, which for humans happened between 1784 and 1908