The attribute is read only and has nothing to do with the permission settings, there is no need to mess with the attributes at this point, it's the sharing tab you need to be concerned with.
You shouldn't be having any problems with read/write access for all the public folders after making those adjustments to the sharing settings.
I even tested this from another machine and I have full control over everything placed into any of the Public folders so the settings we changed through the sharing tab definitely had the desired effect.
I'm sure you can test for full access as well from one of your other machines,. although you may be having other problems with the mythTV access which I'm not familiar with.
It may help to change the path used when you mapped from the myth TV, there are two different paths to this folder from the network, one works while the other won't.
The pictures show that one is shared and the other does not show this. You need to map to the
Network folder \\User-PC\Public when you set up the Myth TV.
Also be sure and turn on Public file sharing in the Advanced Sharing settings via the Network and Sharing Center.