Now, that is a new one on me.
Mary’s traditional typology is the New Ark of the Covenant. She carried Christ hidden from view until He was born in Bethlehem.
The monstrance is a device for exposing the Blessed Sacrament. It shows us Jesus in all His resurrected glory. We can truly see Him and adore His presence.
Mary’s role is more of a tabernacle. The Hebrew’s Ark of the Covenant was a box with a lid. The items inside were hidden from view. It was not for the ordinary person to look inside, just watch Raiders of the Lost Ark for a fantastic tale about that. But the modern tabernacle reserves the Blessed Sacrament. Jesus can be adored here, and we rightly genuflect to Him when we pass in front, but He is not exposed in the same way that He is exposed for Adoration in the monstrance. He is doubly hidden behind closed doors and in the species of bread.
I would say that Christ’s kingship was first celebrated at his Nativity, when the Magi came with gifts. Gold is a gift for a King. I would say that Mary carried him, safe from the world from the moment of His conception by the Holy Spirit. I don’t think there is a basis for comparison to a monstrance.