The Hebrew word שׁכב in Deuteronomy 31:16 doesn't necessarily mean only to "sleep", but it can also mean simply to "lie down" (e.g. Genesis 28:11 KJV). In fact, the JPS Tanakh chooses to translate this verse, You are soon to lie with your fathers.
Regarding Ecclesiastes 9:10, one might also refer to Psalm 146:4:
His breath goeth forth, he returneth to his earth; In that very day his thoughts perish.
It seems not to have been commonly understood by first millennium Christians that all this implied that the soul has a period where it is utterly without consciousness. Dorotheus of Gaza (510-565), for example, maintained that the thoughts referred to in the Psalm refer to "those of this world, about houses and possessions, parents and children, and business transactions:"1
All these things are destroyed immediately when the soul passes out of
the body.
But what he did against virtue or against his evil passions, he
remembers, and nothing of this is lost.
In fact, the soul loses nothing that it did in this world but
remembers everything at its exit from this body more clearly and
distinctly once freed from the earthliness of the body.2
Someone has pointed out, correctly I think, the relevance of Christ's parable of the rich man and Lazarus here (Luke 16:22-28). A 4th century Church Father, John Cassian (360-435) wrote:
If we were to reason on the basis of the testimony of Sacred Scripture
concerning the nature of the soul, in the measure of our
understanding, would it not be, I will not say extremely stupid, but
at least folly, to suspect even in the least that the most precious
part of man (that is, the soul), in which, according to the blessed
Apostle, the image and likeness of God is contained (1 Corinthians
11:7, Colossians 3:10), after putting off this fleshly coarseness in
which it finds itself in the present life, should be come unconscious
- that part which, containing in itself the whol power of reason, makes sensitive by its presence even the dumb and conscious matter of
the flesh? Therefore it follows, and the nature of reason itself
demands, that the spirit after casting off this fleshly coarseness by
which now it is weakened, should bring its mental powers into a better
condition, should restore them as purer and more refined, but should
not be deprived of them?3
But even if the Old Testament Scriptures allude to the soul falling into an unconscious state, this was not necessarily still the case following the Resurrection.
Ecclesiastes 9:10 reads, in the King James translation:
Whatsoever thy hand findeth to do, do it with thy might; for there is no work, nor device, nor knowledge, nor wisdom, in the grave, whither
thou goest.
but the word from the Masoretic Text translated as grave is the Hebrew word, "Sheol" (שְׁאוֹל) - "the Underworld". In the Septuagint we find the word "Hades" (cf. Luke 16:23; 1 Corinthians 15:55; Revelation 1:18). Although atonement is often emphasized as the most important, and sometimes the only, aspect of Christ's Death and Resurrection, the Apostles did not overlook the importance of Christ's descent into Hades during the interim between the Crucifixion and the Resurrection. Peter wrote, for example (1 Peter 3:18-21):
For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God, being put to death in the flesh, but
quickened by the Spirit: By which also he went and preached unto the
spirits in prison
For this is why, Peter adds, why the gospel was preached even to the dead, that though judged in the flesh like men, they might live in the spirit like God (1 Peter 4:6). Paul wrote of how Christ descended into the lower parts of the earth (Ephesians 4:9) and of His victory over death and hell (cf. 1 Corinthians 15:54-57; Romans 10:7; Colossians 2:14-15). Christ as the holder of the keys of Hades is a theme of the Book of Revelation (1:18). All of this suggests that if those in Sheol that the Preacher wrote of were, in fact, asleep spiritually as suggested, Christ's descent into Sheol may have served to awaken them. This is a common theologoumenon (theological opinion) at least in eastern Christianity.
1 Discourses, pp.185-6
2 Ibid.
3 First Conference, Ch. 14