I'm sorry to hear this, James. As the previous "male" in a relationship with a woman in a similar place, I've found myself endlessly frustrated while she doesn't seem particularly phased by our complete lack of sexual intimacy. These days, the T is gone and my drive has changed significantly, but a difference between us remains. When I bring it up, she suggests that the reason is because I don't "do anything". But I touch and kiss her, not in a directly sexual manner, but as a prelude to the next step...and she doesn't signal any desire for anything more.
That's a tough place to be. Unless you believe that a man should just take what he wants (I doubt you do), it doesn't feel right to proceed without encouragement. And as you know, the state of your penis isn't the arbiter of your level of interest in sexual intimacy.
My suggestion is to tell her, in no uncertain terms, that not all men "lead with their penises". She might have prior experience with that as the case, but it isn't always that way, as it's not the case for you. With (I assume) testosterone in your system, you probably don't need much encouragement to get in the mood, but her wiring is clearly different. I think she needs to know that you can/do experience a strong sense of desire without the corresponding physical signals, and that you need her to let you know when there's an opportunity to pursue that, and that you'll most likely be ready to go, no matter what happens to be going on downstairs at that moment.
