The Gazetteer is not a very good source to ID "open" public roads in WY. Strictly guessing, I think the broken line roads are likely 2-tracks, for the most part are open when on public land (but getting to them is the catch 22). If you do not have permission through the private property then you are SOL.
Go ahead and invest in the BLM and Forest Service maps, since you are planning for this year it might be a little to late to gt them ordered and mailed.
If you have a GPS chip and can view it on a computer software, like basecamp, then it can give you a little more detail.
Most named county roads are open, but the tricky part is determining where they end or turn into private.
All I can tell you is when in doubt call the local BLM office or chamber. In all honesty if I were you I would locate public land tracs off of easily ID main roads and plan to hike in from there then when you get out there do a quick drive around to see what other roads are open.
One thing is for sure, there is nothing easy about this part of the planning. Its all trial and error, just hope you dont get a ticket like a bunch of people did a few years ago in 23 when there GPS chip said one road was open when it was actually a private road (which when I was there it had a sign up, so common sense and error on the safe side saved me a ticket).