From the looks of the video the rough section of the road and the lake were in better shape for you than us.
What are you thinking for closed section of the road?
I would say for a group crossing you'd want the lake to be in better shape. A dry month and moderate temps will probably do it.
I guess by 'rough section' you mean that worn downhill section? Yeah that is do-able by anyone with a little articulation and some nerve, it is a little intimidating but very safe. I wouldn't send anyone down with a tall van for example unless they'd had experience and felt comfortable.
For the closed section, the go-around / detour is really a nice drive and a lot of fun. Not part of the official trail but it gets you back on track pretty quickly. I would like to check with the Preserve to see the status of that part to see if it's passable. I wouldn't want to take this many vehicles over it when it's shown as "CLOSED". I would almost like to offer to do some work on it to see if that would make the difference to open it back up or not.
For the lake, I can imagine that it would have been worse but it was so sloppy that the rain that it's had this week has probably made it treacherous to cross and probably extremely difficult. It will need a lot of sun and warm temps to dry out now. I think to send out some adventurous guys that might be willing to check the condition beforehand might be the thing to do. I hate to see a lot of tracks across that area, it becomes sort of a blight. I hated getting off the main track but it was clearly the worst choice and would have made deep ruts there.
And to clean off the mud!? Holy crap, that took me two and a half hours at the car wash and I only got it about 75% done and didn't even touch the interior yet. I imagine I was carrying an extra 400 lbs or so of mud all the way home. It was like cleaning a concrete truck after the cement has dried on. Looked cool, but no thank you. IH8MUD! haha!