Agents or agent teams deployed to assist humans often face the challenges of monitoring the state of key processes in their environment (including the state of their human users themselves) and making periodic decisions based on such monitoring. POMDPs appear well suited to enable agents to address these challenges, given the uncertain environment and cost of actions, but optimal policy generation for POMDPs is computationally expensive. This paper introduces two key implementation techniques (one exact and one approximate), where the policy computation is restricted to the belief space polytope that remains reachable given the progress structure of a domain. One technique uses Lagrangian methods to compute tighter bounds on belief space support in polynomial time, while the other technique is based on approximating policy vectors in dense policy regions of the bounded belief polytope. We illustrate this by enhancing two of the fastest existing algorithms for exact POMDP policy generation. The order of magnitude speedups demonstrate the utility of our implementation techniques in facilitating the deployment of POMDPs within agents assisting human users.