We consider an assemble-to-order system with a high volume of prospective customers arriving per unit time. A companion paper established that with optimal product prices, component production capacity, and sequencing of orders for assembly, the system can be approximated by a diffusion process with dimension equal to the number of components (rather than the number of components plus the number of products). This state space collapse allows us to incorporate product-specific delay constraints and dynamic control of component inventory. First, we choose product prices, component production capacities, and propose a discrete review policy for expediting components and sequencing orders for assembly that satisfies delay constraints perfectly, and is asymptotically optimal when expediting is very costly. We also propose a simpler version of this policy, based on the backlog of demand for each component, that asymptotically complies with delay guarantees and achieves the same limiting expected discounted profit. Second, we numerically solve an approximating diffusion control problem for systems with both expediting and salvaging of components, and highlight useful structural properties.