If it were me I would depart the Iron Horse trail in Cle Elum and then go SR970 to SR97 to SR2 to Spokane. Due to closure you would have to detour from Cle Elum to Thorp anyway. The Vantage Bridge (I 90) does not have a shoulder at all. I've ridden it myself and know others that have however near 4th of July there will likely be lots of traffic which will make it fairly unsafe. Blewett Pass is on the other hand a beautiful 2-3 lane highway. The Wenatchee valley is also beautiful. There are two bridges that cross the Columbia in Wenatchee, as well as I think a MUP bridge. From East Wenatchee you can go through Quincy (SR28) or follow US 2 up through Waterville and Coulee City with attractions worth seeing close to Coulee City; Dry Falls, just a few miles from Coulee City and Grand Coulee Dam 35 miles North of Coulee City. From Coulee City east the towns are about 10 miles apart with a jump of 20 between a couple of them.
The SR 28 route you could also see the Grand Coulee, upper and lower by going east through Quincy and then Ephrata and then North through Soap Lake and take SR 17 to Coulee City passing right by Dry Coulee. Or follow the I90 corridor through Moses Lake, meh and Lind, Ritzville, Tokyo. Some longish stretches between waterholes and limited camping opportunities. Or just follow SR 28 out through Wilson Creek and Odessa, Harrington.
It really matter how much time you want to take through Washington. Ellensburg, being the center of the world, is a great place to stop and visit. We have an awesome micro brewery, Iron Horse Brewery. A handful of good restaurants. A well stocked LBS with a friendly staff. If you came through here and still wanted to avoid the Vantage Bridge, you could go south through the Yakima valley and the Tricities before going back North towards Spokane. There really are a number of possibilities depending on how much time you have and what you want to see. Any other questions please ask. I've driven over all our cross state routes. Ran the US 2 route years ago as an Athletes VS MS run although I've not cycled it. I have cycled Blewett Pass and Ellensburg to Moses lake with two different routes in Grant County I90 and SR281 to SR 17.
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Sir Mark, Knight of Sufferlandria