How can I meet the height requirements for a door in a basement with a low ceiling?
Ask your Local Authority Having Jurisdiction -- eg, your town's building inspector. You may have a grandfathered situation. Or, if this door is not considered an essential exit from a living space (if it's an unfinished basement, for example, or if sufficient other exits exist), the headroom requirement may not apply -- you may be able to argue that requirements are already met and this opening does not have to comply and get a written variance. It's really going to be a question of the inspector's judgement.