The Lord teaches that in heaven we neither marry, nor are given in marriage, but are "as the angels," that is, the earthly kind of relationships do not extend into the greater heavenly reality.
"Till death do us part" does not verbally exclude the time after death. In Matthew 1:25 it says of the virgin Mary that Joseph "knew her not" (did not have sex with her) "till she brought forth her firstborn Son." That does NOT mean that he "knew" her afterwards; on the contrary, we teach that she is Ever-Virgin, a virgin before, during and after giving birth.
The giving away of the bride is a custom of the old Roman rite and is found in the Eastern rites as well in various forms. It is a change of one man who was the protector of the vulnerable female, to another protecting man. How far that ultimately derives from "ownership" concepts is quite debatable, but it's a stretch to take it in any literal sense, just as the injunction for wives to obey their husbands does not mean they are slaves.
The service is an ancient one, the main features of which are found in the 1st century and more clearly in documents of the 8th, 9th, and 10th centuries. It requires no revision to be in the fullness of Orthodox theology.
The crowns are an ancient part of the Western service but are not as prominent in that service as in the Eastern rite service. Therefore, the crowning custom sort of diminished over time in the West. By the end of the middle ages, often only the woman had a crown (wreath), and nowadays even that has been lost from the modern Western rites. By no means are they a Byzantinization of the service; the use of metal crowns for the bride and groom is mentioned by Pope Nicholas I of Rome in the middle of the ninth century for the Roman rite.