A week is a bit much I think. The mechanism at work is that the game calculates things differently when it's playing 'catch-up' when you haven't played a while, and it's more likely for a villager to reach an older age during these times. There are no guaranteed methods, only likelihoods.

Look at the advice given for people waiting on collectibles; don't play to get a collectible, or play to 'win'. Just play because it's fun to play. Many of the achievements that are so frustrating are only a matter of time. If you don't obsess over them, they'll just turn up completed one day; the Ancient Elder award is one of these that I seem to always complete without realizing it.