I've been having a bit of fun with Gillian Speedy's dialog. As well as filling in questions for Purpure's answers, I've written some default lines - it's usually a good idea to have something just in case you meet the character while she's not doing anything specific. Usually this will be something simple such as an exchange of "Hello". Gillian will say "Behave yourself, Miss Longstride! I am watching you". But if you have a British letter of marque, what she says will depend on your rank. If Gillian outranks you, which is likely because she commands at least two ships so she's at least a Commodore, she says "Stand to attention when you speak to me, Miss Longstride!", though once you've earned a promotion, she'll address you by rank, e.g. "Stand to attention when you speak to me, Lieutenant Longstride!" If you're her equal, it will just be an exchange of "Good day, Commodore". If you have been playing full on privateer and actually outrank Gillian, she'll say "Have you any orders for me, ma'am?" Of course, none of that is for the interrogation scene, where she asks my questions and Purpure gives your answers.
Next: play as Purpure long enough to trigger the arrest and interrogation, then write the code for Simon's rescue and a chase across Nevis to the pirate settlement, where Purpure will get the Lotus.
Update: the chase is on! After Simon releases you, you go into the town and then through a sequence of jungle locations until you reach the pirate settlement. At each stage, Simon runs along the path to the correct exit to the next location, and you'd better keep up because Lucretia is following. If you take a wrong turn or double back, Lucretia will catch you. And about 10 seconds after you enter a location, Lucretia follows and runs after you. Either way, if she catches you, you and Simon are both sent back to prison. Simon tells you off, then Purpure herself tells the player that she and Simon are now stuck so you may as well quit the game. But if you outrun Lucretia and follow Simon to the pirate settlement, you'll get the Lotus, and any officers who were with you before the arrest now rejoin you - they got away, it was only Purpure who was imprisoned. Simon also joins you as an officer.
I'm assuming that at some time in the future, Purpure will find the impostor, bring her to justice and clear her name. So your ship and any rank you may have with Britain are stored at the time of the arrest, so that they can be restored later.