We drove in by the "alternate route" from the Black Velvet road, taking the first left after ~1 mi, then going to the T-intersection, and taking a right. There's a bit of a rough "down-up" just before the parking area but most 2WD's could probably do it.
We drove out by the usual Windy Peak road, via the "narrow wash" that parallel's Hwy 160. There were some sections of this that might be difficult in a 2WD, and I wouldn't recommend it.
If I did it again, I would just go in and out by the Black Velvet alternate route. It's longer, but a lot easier on your car. I have a 2011 Outback and the alternate route was cruiser.
I did Jubilant Song last week and the road was rough but didn't look like from any flooding. The road is just rocky and rough. We were in a 4WD Subaru, but I think a 2WD would get it done.