The King James Version says that God "winked at" their ignorance.
The word is unusual - ὑπεροράω. It appears only here in the New Testament, but is a little more common in the Septuagint, where it pretty much means what the English words "overlook", "ignore" or "disregard" do. It is sometimes translated in Brenton also as "despise" and "neglect". Examples:
Leviticus 20:4 LXX
And if the natives of the land should in anywise overlook that man in giving of his seed to Moloch, so as not to put him to death;
Isaiah 58:7 LXX
Break thy bread to the hungry, and lead the unsheltered poor to thy house: if thou seest one naked, clothe him, and thou shalt not
disregard the relations of thine own seed.
Numbers 5:12 LXX
Speak to the children of Israel, and thou shalt say to them, Whosesoever wife shall transgress against him, and slight and
Sirach 38:16 LXX
My son, let tears fall down over the dead, and begin to lament, as if thou hadst suffered great harm thyself; and then cover his body
according to the custom, and neglect not his burial.
Psalm 77:62 LXX
And he gave his people to the sword; and disdained his inheritance.
That those ignorant of the Gospel will be called to less account is a firm teaching in Scripture. We have, for example:
But he that knew not, and did commit things worthy of stripes, shall be beaten with few stripes. For unto whomsoever much is given, of him
shall be much required: and to whom men have committed much, of him
they will ask the more.
The theme of this passage is discussed in the early Christian Epistle to Diognetus (Ch. IX):
As long then as the former time endured, He permitted us to be borne
along by unruly impulses, being drawn away by the desire of pleasure
and various lusts. This was not that He at all delighted in our sins,
but that He simply endured them; nor that He approved the time of
working iniquity which then was, but that He sought to form a mind
conscious of righteousness, so that being convinced in that time of
our unworthiness of attaining life through our own works, it should
now, through the kindness of God, be vouchsafed to us; and having made
it manifest that in ourselves we were unable to enter into the kingdom
of God, we might through the power of God be made able.
This is a forum for exegesis and not theology (though the two frequently intersect), but I do not think your statement that "according to most orthodox Christian theology, these pagans who died without Christ are forever condemned and without hope" is correct. Such a believe would actually be contrary to Scripture and negate the meaning of Christ's death and resurrection, wherein He descended into Hades and preached unto the spirits in prison (1 Peter 3:18-19; also cf. 1 Peter 4:6, Ephesians 4:8-10).