Birdie, welcome to CDH. I am a crossdresser and also conservative. As others here have already said I am troubled with Deut 22:5. BUT I have come to terms with that for now. I did cross dress behind my wife’s back off and on for many years, we are now divorced (nothing to do with cross dressing).
If you are correct in that he is still lying to you then he has a problem and is probably afraid. If the both of you don’t receive councelling and him seperately you are likely doomed. Your spouse has spend sooooo much of his life in hiding and in SHAME that it is very hard to be 100% truthful to you 100% of the time. With councelling and the desire you say you have to understand all of this and work through this we all hope you can be saved .