In all honesty I'd walk away from this one.
Personally, I wouldn't be happy dating anyone who hadn't at least started divorce proceedings, and ideally I'd prefer the divorce to be settled. There are important legal reasons for this, as well as emotional ones.
The next of kin one is one reason. Liability for debts is another. Not being free to legally commit to a new relationship is also a factor. If divorce is not a big deal, why is marriage?
Emotionally, it has nothing to do with feelings for the STBX, which have often long disappeared, but even people who have long felt nothing but indifference for their X have a period of adjustment and reflection following divorce. It's not unheard of for someone who is going through a divorce while already in a new relationship to suddenly find after the financial and emotional turmoil of divorce - especially a difficult one - they suddenly find themselves wanting to spend some time single. Or they want to ease back on the seriousness of the new relationship. Or they are suddenly commitment phobic, especially when it comes to money. All of which are perfectly normal and healthy reactions to getting divorced but are not conducive to a good start for a new relationship.
In the real world, of course, lots of people are already in new relationships before the ink on their divorce is dry (if they've even started it). Sometimes it works out, sometimes it doesn't.
However, your massive red flag is that he's already had one long-term relationship end over his refusal to get divorced. He is not going to get divorced. Accept that and know you cannot change it.
The question you need to ask yourself is do you want to be anything other than a casual girlfriend? Because that's all you can be.
BTW, just another thing to consider. If you are living together at your house, is he having mail delivered there and using your address as his official residence? Because if he is, his wife's credit rating could affect yours because of his link to her by marriage and his link to you by shared address.