You know I have followed you from the beginning as we showed up here around the same time. Maybe I am too close to your story to have a good outsider's perspective but here goes my 2 cents!
If you were my real life friend and we were having a tea and discussing your situation I would probably recommend two paths (that you already mentioned).
1. just live your life, forget him and start dating - let go of H completely and see how this plays out for you or 2. change your game and start reaching out to him as a "friend" but be prepared for yucky truths
Option 1 It is possible if you just let go and "move on" that you will allow yourself to discover you'd rather be with someone else more compatible. One thing you said resonated with me. I think it was about being with someone who would take your hand to new adventures. I am starting to feel this way myself. As much as I was happy in my relationship would I be happier with someone different? Maybe you need to allow yourself to find out? I know you are married and likely don't feel right about dating. If you think of it as just being open to meeting new people of the sexy variety maybe you can get past it for now. As someone else said, you don't need to start a relationship, just have coffee or drinks or walks or do yoga. But be open to possibilities of connection. However, maybe you don't feel right about that and that would also be admirable. In that case I think Option 2 might be better.
Option 2 My advice would be to reach out to him. As others have suggested you could do it in a friendly way, just suggesting random activities and opening up a line of communication. I feel this could work to create rapport. The other option is to directly ask him where things stand. I think in either case, communication opens the possibility to hear something negative which may or may not help you to decide what to do next. Believe me, finding out there is OW might seem like useful information but may just add another dimension of unanswered questions and pain. It may not help you to move on or withstand NC. It may just be painful. On the other hand you might hear some negative news and pull yourself together and move on.
Continuing to do nothing I think is not the best idea for you at this point. I feel although you seem to be doing very well and are GALing amazingly that you are still waiting around. And that waiting energy is not the right energy - it is not dynamic. Maybe I am not explaining it very well, but I have been living it. I have been waiting for my H to get over his OWs and wake up. But that is not the right energy to put out there. It is stagnant.
I've written on other threads about some of my real life friends who have reunited after long separations. One thing most have in common is that they dated other people while apart. They tried to "move on". Some got into serious relationships. In the end they found their way back to each other somehow after learning that the grass was not greener.
That's my two cents, maybe biased by my own current feelings. We all look forward to your next thoughts!