Hairy, Correct me if I'm wrong, but haven't you BEEN showing unconditional love to her for the last several years? Sex a handful of times per year and you're there and still love her. So why hasn't this increased her feelings of wanting to try?
Furthermore, the idea of unconditional love is just bogus.
I can guarantee that if you started beating her, she'd be outta there. We ALL have boundaries and conditions that must be met. Understand that I am not equating being sex starved with spousal abuse--merely stating the obvious that she does indeed have conditions but sex just isn't one of them. Perhaps if you said, I will help around the house maybe 2 times per year. The rest of the time you are on your own.
I can further guarantee that she'd find her commitment to you and the R wavering and she'd be left wondering what she gets out of this R, anyway.
As far as Mr. Peckerhead and his views on Love, well, there are about a zillion more books that tout lotsa love as a relationship salve than ones like his, so if she wants to get into a book war, bring it on!
What does your C say about unconditional love? I think your W would benefit hearing from a third party that this is not something to strive for in an adult relationship.
However, having said all that, I do get what your wife is saying. She can't find it in herself to try because she feels she's being graded.
My only suggestion around that is to make a schedule. Saturday nights are for luuuuv. That way, she doesn't have to worry about it, or think of excuses, etc. It sounds like someone with her rigid personality would also benefit from knowing the what, when and where, too. IOW, what is expected of her.
Can you bring this up in counseling and see how it goes?