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The "period of time" bit is particularly relevant to the latest news items I posted above. One of the new assumptions (or relaxation of assumption) involved in this recent study was considering that a sufficiently advanced civilization might be stable enough to wait literally ages (as in millions of years) so as to allow interstellar movements to reduce the distances they'd need to travel. All the stars and star systems are moving relative to each other - some at higher speeds than our own Sol.
You do know that it appears all the galaxies are moving away from each other at an increasing velocity ?
So your ET will have even further to travel, not less.
INT21.