If you had asked me a week (just 1 week!) ago whether I was LD or HD, I would have definitely said LD. For a long time, I have not wanted any type of physical intimacy with my H. With that being said, I have just recently read 5LL and gave my H the "reader's digest" version. We both took the quizzes at the end, but I already knew what the results would be before we did so. My H is primary Physical Touch, secondary Words of Affirmation. I speak two LLs, Receiving Gifts and Acts of Service (1 point apart on quiz). I answered just ONE question for physical touch. After reading the book and realizing just HOW important it is to him, I have decided to be the one to start the change, even though just a short while ago, I was ready to walk from my marriage. I have started doing things for him that I don't enjoy in and of itself, such as giving massages or initiating ML. BUT, my desire to love him in his language is very strong. So, I do not think it is difficult to be genuine if you truly want to make that person feel loved.
I think all of us yearn to be loved. And I know that in order to receive what I need from my H, I have to start fulfilling his needs. While I am still harboring a little resentment for being the one to start changes when I was the one who wanted to leave, I am without a doubt trying to do my very best to save my marriage.
With that little experience being shared, I want to encourage you to take a long look into yourself and be the one to step up to the plate and love your wife in her language WITHOUT expectations. And when the time is right, when her "love tank is overflowing," be candid with her, not accusatory or demanding, and explain your needs and LL... encourage her to read the book.
One thing you really need to get over is the "desire for sex" versus the "willingness for sex." You need to recognize that your wife may never feel the same way as you towards physical touch and intimacy, but that does not change the fact that she is or would be willing to love you in your LL.
Although, I am now unsure if I am LD or HD, I do know that I desire to please my husband and speak his LL. I now give him little random hugs, offer to massage his back without him asking, and initiate sex. The activities themselves I do not enjoy with the same intensity he does (not even close!), but my H recognizes these for what they are, acts of love. And he responds in kind! He is starting to do little things for me without grumbling or me asking. These are things I know he doesn't enjoy, but he desires to show me love in one of my languages. These actions makes me want to show him more love! It is a wonderful cycle! Willingness to have sex or show affection when it does not come naturally is one of the most ultimate expressions of love, imho.