Toddler Crying After Naps
You write that he "wakes crying and seems disoriented and almost like he is not at all awake. He has a lot of trouble calming down afterwards, too ..." This is a good description of sleep inertia, the intrusion of sleep into wakefulness following "awakening" (especially from a nap) and represents an altered state of consciousness in which he may move about and speak but is not fully aware. It is uncomfortable or painful. Some napping toddlers do not show this full-blown state but simply cry upon awakening from a nap. The intensity of pain and the duration of the abnormal state is increased with increasing preceding sleep deprivation. So whenever this is going on, you know that your child is sleep deprived.
As you stated, "We've tried putting him down a little earlier at night ..." without alleviating the sleep inertia. If a little earlier bedtime did not help, probably it was still way too late so you saw no benefit. Try a reset, and a much, much earlier bedtime to see if this helps. Watch for drowsy signals, but they might be absent if he is way sleep deprived.