Did King David rape Bath-sheba?

[Tonus]

David had another child by her, and made that child his successor despite him not being the eldest. This indicates to me that David had love and/or respect for her, and is further reason to doubt rape.

That's... kinda creepy. Though it makes for a more interesting story.

This is again an argument from silence. David could have been punished in many ways that would have had no effect on Bathsheba. The death of the child presumably hurt her. From this we can infer that she was being punished as well. It's circumstantial, but as you agreed above that it was likely consensual and not rape, this explanation fits well.

I was thinking on this one and I think the best explanation is that it's a plot hole, at least from my perspective. But I think yours works if we have to make it work, in that your explanation holds up (IMO).

It was as I was considering that last part that I realized that Bath-sheba really is just a prop in the story. The foil in this story is Uriah; it is his decision (to show a sort of spiritual solidarity with his brothers on the battlefront) that leads to David going from a man who suffered a moment of weakness to a man who allows his inner demons free rein and brings Yahweh's anger crashing down upon him and his house. Bath-sheba is so incidental to the story that the writer never bothers to consider her thoughts or feelings, and so we know almost nothing of how she reacts to anything that is happening. And we're not supposed to: David is the character that matters.

Perhaps the same writer wrote Solomon's story, as we see a bit of similarity: a man who rises to greatness as a testament to Yahweh's strength and power, yet eventually falls in disgrace. David at least seems to gain a measure of redemption, but I don't think we ever learn of Solomon's fate, save that he eventually abandons Yahweh and serves lesser gods.