I think it is an overstatement to say that the word is only used by Mary and the Ark in the entire Scripture.
The same verb is used in the accounts of the transfiguration (Matt. 17:5; Mark 9:7; Luke 9:34). Kittel in, Theological Dictionary of the New Testament, did mentioned:
The literal meaning “to overshadow,” “to cast a shadow,” occurs in Act 5:15. In the background is the popular view of the apostle Peter as the person who heals all sickness.
In the Old Testament, it also occurs in Deuteronomy 11:12, Psalms 91:4 and Isaiah 32:14-17.
The parallelism for David's fear of the Ark versus Elizabeth's joy in acknowledging the divinity of the child seem stretch.
Also, the Greek word, skirtao, tends to be associated with "the movements of the
child in the womb" and "these movements express joy, jubilation". Kittel mentions:
Two motifs control the use in Luke: the natural movement of the child in the womb, and eschatological joy at the coming of Christ. The former is prefigured in Gen 25:22 the latter in Mal 4:2, where the comparison gives expression to joy at eschatological
Both are the Hebrew equivalent of the Greek Word, skirtao.
If I will be generous, it is the proximity of Mary next to Jesus, as the reality of the type of the Ark of the Covenant, that these passages seems "similiar".
EDIT: It would seem that I will now hold the assumption that the exact conjugation holds.
If so, there must be consistency of the interpretation of the types. A type (Gk. typos, from typtö,
“to strike”) is a stamp, pattern, or mold, indicating that a pattern or idea is applied to someone or something else. The analogy of a typeface in printing and its corresponding
image is helpful.
Types may be persons (Adam), offices (the priesthood and kingship), entities (the tabernacle), or events (the Passover and Israel’s wandering in the wilderness).
Traditionally, David is a type of Christ and to associate it with John the Baptist is stretching it. And again, the same argument holds to David as a type of Elizabeth.
With this, I would not be surprised if most writers outside of Catholicism have even consider the similarity (in my humble opinion) when the types of Christ is more outstanding and consistent.
Below are some of the writers:
Benjamin Keach (1640-1704), a Baptist, wrote in his book, "Preaching TYpes & Metaphors):
THE ARK A TYPE OF CHRIST
The Ark was an assurance of God's presence amongst his people : so Christ is the cause and assurance, that God in a gracious way is present with us. Where the Ark was, there it was lawful to offer sacrifice, and no where else: which might show that our acceptance in God's sight, is through Jesus Christ.
Kenneth E. Trent, in his book, "Types of Christ in the Old Testament", quoted:
The ark is one of the most dramatic and outstanding types of Christ found anywhere in the entire Bible.
Charles Spurgeon, in his sermon:
Let us think of what was in the ancient ark of the covenant, for all that was in that ark as a type is to be seen in Christ our heavenly covenant ark above.
In that ark, if you and I could have gone into the holy place, and have had our eyes strengthened to look. we should have seen, first, God dwelling among men.
John Wesley, makes the connection:
"...between Christ, on the one hand, and the mercy-seat of the ark of the covenant, on the other, which, as a propitiatory covering, was "a type of Christ the great propitiation" (The Theology of John Wesley: Holy Love and the Shape of Grace)
Charles Henry Mackintosh, from The Mackintosh Treasury:
Thus we perceive what a marked type the ark of the covenant was of Him who magnified the law and made it honorable - even Jesus the Son of God ....
John Nelson Darby, in the synopsis of the Bible:
The ark of Jehovah passed over before the people, who were to leave the space of two thousand cubits between it and them, that they might know the way by which they must go; for they had not passed this way before. Who indeed had passed through death, to rise beyond its power, until Christ, the true Ark of the Covenant, had opened this way?