As soon as you can, get rid of the run-flats. I-90 on this side of the mountains will destroy them. If you're relying on Costco to replace (because they can't be repaired) them, be aware that they are booked out at least one month, so you'll either be running on a spare for a month or your car will be immobile for a month.

This advice will be jeered, but the best way to avoid blowing out your tires is to stay in the left lane from Ellensburg to Issaquah.

As for snow, just take it easy and you'll be okay. Bring extra water, snacks, and a warm blanket, just in case something does happen.