Hi! I believe I can be of help with this issue.
First, let me say I can imagine how frustrating and distressing this situation must be for you. You are clearly a capable and intelligent woman and so I am going to be open and honest with you.
You've described this as a situation that only allows for you two to be in conflict. He wants what he wants; you want what you want, and by definition the two wants are in conflict.
The first thing we have to do, then, is to change this dynamic, okay?
He doesn't want therapy, he doesn't want what's healthy. It sounds like he's trapped in his job and trapped in his life's routines. You don't want to keep going on as it is, you don't want to have a totally unromantic marriage. It sounds like you're also trapped in your life's routines. Or rather, his life's routines.
So, make an approach TOWARD him. Don't keep trying to pull him out of his isolation. He is trapped in there. Make a move toward him: ask him if he would be willing to spend some of each of those 3-4 days/month with you by his side? If he would let you be there in his "cave" with him? Would he hold hands while watching TV? Would he read some of the internet articles to you?
Don't keep trying to pull him out; you find a way to share his cave with him. And if he lets you in a little at a time, you can then ask if he'd give you half an hour sometimes? Maybe watching an exercise video with you. Or maybe watching a motivational speaker with you:
Some like Tony Robbins are the classic big guys. Some are newer. There are now great women speakers as well. Watch them all. Get inspired. Buy a book or two. Here are some possibilities, but they are only suggestions as there are so many good ones.
Communication is the muscular system of love. And love is the circulatory system. Let me repeat that because it's so important: it's not sex; it's not beauty or looking good; it's not being smart or clever. Communication between the two people is the love muscle; it's the muscular system of love. The desire to give to the other person, to make the other person happy is the heart of love, the circulatory system.
Your husband is feeling trapped in his life and needs to withdraw. The communication between you two has been lost. So, when you're in there with him, we'll also try to see if we can get him to be willing to put his "heart" back into this, to reactivate his giving circulatory system.
You're going to start with a book. You'll get 2 copies, one for each of you. Each night you're both going to read a few pages or a chapter and do the exercise there if there is one in those pages. Every other night, or at most, every third night sometimes, you will get together, either at home or at the Starbucks and talk about what you read. What you think of it, what it inspired in you. Make notes in the margins. And each one talk about the subject of the pages and what you think. That's your assignment and dates. This is for after you've started getting a little more together.
The book: It's by the foremost researcher into relationships in our day, John Gottman. He's famous for being interviewed on TV and being able to tell when a couple will get divorced within 5 minutes and having 90% accuracy. I've studied his therapy and use his therapy in my practice and that's why I'm concerned that you two do this. So the book is the Seven Principles for Making Marriage Work. You can get it cheaply online or see if you can get it locally to save time.
Now, a secret: the magic is not in the book. The exercises and Gottman's insights will be very useful and important for the two of you. But the magic is in the act of working together on your marriage! The two of you paying attention every single day to your marriage and making effort every single day: that's the magic ingredient in great marriages that GROW in love as the years pile up. I want to make sure you both understand this. Because that's the key to our work here. Okay?
If this work gets you two to first base but not all the way, if it isn't a home run, then at that time he might be willing to consider therapy. So keep this for the future. One type of therapy is called Emotionally Focused Couples Therapy. Why this type for you? Because it focuses on how there have been created emotional barriers and how to get through those barriers. Here is the web address for their therapist finder: http://iceeft.com/findtherapist.php
On the website you'll also find excellent books by the founders, Sue Johnson and Leslie Greenberg.
There are not that many therapist who work in these therapies and so I recommended EFT couples therapy knowing that often it's a way to orient you on the type of work you want the therapist you do choose to focus on. Because whatever couples therapist you go to, you need to use the framework of my answer to help guide the healing between you and your husband. There has to be a recognition of what truly is the problem here.
Here is the web address for Psychology Today's therapist directory. You can sort by zip codes and when you see someone who seems like they might be helpful (they show you a photo of the therapist!) look at the listing and see if they list couples therapy in their orientations. Interview the therapist and make sure he/she shares your values and you each feel confident in him or her. http://therapists.psychologytoday.com/rms/
Okay, I wish you the very best!