The last non-lottery permit weekend is likely to see more people out there, so you will probably have company.
Just so you know... Mt Muir is an hour's walk to the south (and back if you plan to descend the MR). You could always make it a loop trip and descend the Main Trail.
Mt Muir sticks up so much, it will likely be nearly snow free, so if you have the time, it shouldn't be much different from a summer ascent.
