Your plan is awfully ambitious.
Day #1...I'd go over Army Pass...it more direct and less climbing. This gives the option of doing Langley on the way in. The Miter is a long way after a day of dealing with sand and up and down of the CL/NAP Trail. If you want to use NAP, take the South Fork Trail after the first stream crossing the unmarked junction is about 180' beyond the crossing. This will cut about a mile off the distance to NAP. You will have to some easy cross country hiking through the South Fork Lakes basin, consult your map for the logical route back to the NAP Trail below Long Lake.
You can spend the night at Lower Soldier Lake, if you are whooped.
Day #2...It sounds reasonable.
Day #3...I hate the hike back to Cottonwood Pass. I only time I'd do it would be if Army or New Army are closed because of snow. It is too sandy and too up and down. Also, consider looping out over Trail Peak and Trail Pass. If you are strong enough to reach the Miter on your first day, this should not create a problem for you. This is a much prettier way to go.