Is 我很对不起你 a unique sentence structure?
I think the Chinese language has always been very consistent here. Consider the following:


我很对不起你。
我很讨厌你。
我很爱你。


The subject-verb-object sentence structure is very consistent. In English, the last two sentences can be translated directly with:


I hate you very much.
I love you very much.


The reason why the first sentence could not be translated directly is due to the lack of such a verb in English and not due to the peculiarity of the Chinese language.

The third meaning in the Wikitionary article you quoted captures more of the essence of this verb "对不起" than the first two:


  to do something to a person that would demand an apology later on


To elaborate, "我很对不起你" is not a statement of apology but a statement that you owe someone more than just an apology. This is logically so, because the subject would have easily apologised with a simple sorry (对不起) when speaking directly to the other party.

To extend this further, "你很对不起她" is another valid statement to mean you owe her more than just an apology. Example:


  她为了你付出了这么多，你却这样糟蹋她。你真的很对不起她。
  
  She has done so much for you, yet you treated her so badly. You really
  owe her more than just an apology.