According to Bears Ears Ranger District, the gate at the forest boundary remains closed until July 1. It was open when we sledded by it, with 2 feet of snow around it. I guess they will close it when they can. It's vital bird habitat. That's why the gate remains closed so late.
The take-out is on private property, a second generation ranch called Elkhead Ranch. The landowner lives right beside the take-out. If you park a vehicle at the bridge, the landowner will know what's up. They will be unhappy! You need permission from them if you want to take out legally and without ruining further access to this river. They are nice people, but would feel really insulted if you didn't ask permission first.
I doubt this run can be done without snowmobiling in or a 3-5 mile hike over/around Quaker Mountain. I am not sure though. I suppose it's possible that the gate will remain open after the road is clear. If so, you could theoretically drive to the putin. There is a lot of snow up there still (8600 ft).
Here is your gauge: http://nwis.waterdata.usgs.gov/nwis/uv?09246200
It has been running since mid-April and will probably go through May. Who knows? We did it on the 29th. It was probably above medium, maybe high. I would think it would go a lot lower. The flatwater might suck though.
you will need your gazetteer