That route adds almost 150 miles vs. taking I-40 to Amarillo and then cutting down US-287 via Fort Worth. What is your reasoning for taking this new, longer route?

Are you still planning to spend the night after the Grand Canyon in Flagstaff? If so, you're back to needing 2 nights to make it to Houston. You'd want to spend your first night in Las Cruces or El Paso, and then spend a second night in San Antonio, before finishing the last 3.5-4 hours to Houston on day 3.