> With time dilation, the "now" on Voyager is out of sync with our now

A couple minutes [1].

> we will have to face the problem of time keeping across the galaxy

Not really. Barring relativistic travel, it’s not dissimilar from the problem seagoing voyagers faced on long trade routes. Ship time is set based on the convenience of the passengers and the route.

[1] https://space.stackexchange.com/questions/56055/if-voyager-1...