So, I took myself up on my own challenge lol, and did a study last night. I cannot find a single verse that anywhere says parents have ownership over their children, or that the parents' desire/intent matters in forming a marriage. Firstly, that seems contradicted by the spirit of every OTHER verse where God says that single/divorced/etc women can choose 'as they will'. Does He not care about their will as long as their parents live? Seems silly to think so.
Payment does not imply ownership to me, it implies a resource. The daughter is a resource to her father as a helper and family member who was going to help do work and things. The payment is to make up for that loss. But note that nowhere is a specific 'bride price' described (so God doesn't care about the amount) and nowhere is that required for marriage...it's simply required to 'honor thy father and mother' it seems to me.
And actually, Numbers 30...it is NOT exactly the same...because while the HUSBAND can nullify a vow made for marriage, the father cannot.
(Numbers 6-8)
I like cnystrom's image that a daughter is like an employee in the family business. Of course her employer tells her the expectations for the job, but that doesn't mean he owns her soul.
I would do my absolute best to never tell my daughter to or not to marry. I would instead seek to cultivate a relationship such that she respected my wisdom and opinion so much that she would trust me and seek it out when analyzing a marriage partner, and that my opinion would carry great weight in her decision. But I would not command: I don't believe fathers have that authority. And I have yet to see anyone prove it in scripture. In fact I really don't see anywhere in scripture where that sort of 'arranged marriage' (obviously not really, but you know what I mean) is instructed by God. I see a few examples of it happening (Isaac, Samson, etc) but all the times that I see God speaking of a woman marrying, it refers to her own choice. I'd argue that where it was allowed, God worked within the culture of the time, similarly to how He worked with their desire for a king (but clearly never intended them to have one to begin with).