Respectfully, I'd suggest Jesus fits the typology of what was *in* the Ark rather than the Ark itself. The following were kept in the Ark of the covenant according to Jewish tradition: the tables of the Law, and a portion of manna from the desert. Christ is the perfect fulfillment of these Old Testament types. The Word made Flesh more excellent than the Law, the Bread of Life more excellent than the manna of Moses (as Catholics we have a very literal view of that passage too, but I don't think you have to: Christ Himself made the equation in John 6)
And it follows naturally, that as Mary was the vessel of Christ's Incarnation, she is the typological fulfillment of the Ark. And since it would be strange indeed that an OT typological predecessor be *more* excellent than the NT thing it was pointing toward, it is a good bet that Mary surpassed her Old Testament archetype in purity and perfection. Is it a proof of the doctrine? Not really--but it makes the most sense of all of Scripture when read this way.
Plus, as people have already pointed out, Mary as the New Eve and as the Ark was a common equation made in the early church, and is implicitly taught in the Revelation of St. John. If Mary as the Ark takes away from the glory of Jesus, why didn't the golden Ark itself take away from the Law which it housed? I think Moses would argue that the Ark was made beautiful *because* of what it was to contain. And Mary was made beautiful (by her own Son!) for the same reason. Mary's light, like the Ark's, is only reflected--she merits all her honor through her Son.