No permit is currently required at the #1587 trail head, as indicated by a FS sign.
Correction noted. Thanks for catching it.
Your weather forecast link is for Snoqualmie Pass, but Stevens Pass would be more accurate considering this is Highway 2.
When I checked weatherunderground the closest link I could find of Snoqualmie Pass. I will check again, but they did not have Stevens Pass the last time. Good catch though.
I believe that town, which is after Stevens Pass but before Leavenworth, will be your closest option. Otherwise, Leavenworth would be the next best option after that, since Stevens Pass is not usable.
I was out there yesterday and many large sections of trail between 4600' and 5000' are totally wiped out as you can see in this photograph. Route finding whether you go left or right around the debris is tricky. We tried both ways. On ascent I would suggest going as far as possible on the trail through the meadow. Then look for a small piece of flagging hanging for a tree branch. Cross over the log pile and the trail will be on the other side. For the next sections that are impassable, always skirt to the left.