Well how about that? I got out a fresh game so this one will count.
This game that comes out is number 0210843428856.
I'm going to give you more or less complete instructions for getting this one out. Take every card you can with a few exceptions. On the original deal, don't take the last Black Queen you can, or the Black 6, and don't take the first ones that come out on the redeal either. Also, don't take the last Red 5 or Red King on the first deal.
I did work this out with a lot of undoing, but it might be (I haven't checked) that you could work this all out analytically on the first run through. After the first deal is complete the game is open, even though it is not played as such. It may be that the moves I didn't make (after in fact making them and then unmaking them) could have been seen that way the first time round.
I suspect this game might be get outable more often than I thought. I had only three failed games after my last success, which was why it took so little time to get it out. And I didn't play those through, just gave them up quickly. If it does come out often, it will be by the kind of analysis (or undoing) that I did this time.
Quite happy about this one. I feel like I understand the patience a lot better now, and it may not be completely unbearable to play again.