Thanks for testing it out. I appreciate getting verifications about my methods.I have tried it and it works. Though, if you follow the choices on your screenshots there isn't much difference to what Achilles' walkthrough suggests.
You start at 50.
+8 influence for being nice to her during the holorec cutscene.
http://i41.photobucket.com/albums/e288/JediShemL/Handmaiden%20Progress/HandD12.jpg)
+8 Winning the first duel.
+8: When she asks about your trial choose the line about your hatred for the Jedi for influence and DSP:
http://i41.photobucket.com/albums/e288/JediShemL/Handmaiden%20Progress/HandD23.jpg)
This conversation may come up either after the first or the second duel. If she asks you about the trial after the first duel, there will be no conversation after the second one. If she asks you about how the Force feels first then she will ask about the trial after the second sparring match. That is what the walkthrough describes. Looking at how the global 000_Handmaiden_Force is handled, I assume if you didn't tell her about the Force in the academy already, she will bring it up after sparring with her.
Except for "I guess I thought maybe they could help me." (R398) all replies can give you influence here. In any case, no major difference between the walkthrough and the screenshots.
I hope that solves the first 16-point mystery. :)
+8: Win second duel
+8: Ask her why she looks different than her sister.
+8: Win third duel.
After the final sparring match a new conversation option will be available: "Then maybe I can teach you some things." (R262). If your influence is greater than 74 or less than 26 (E187) she will tell you that her father has broken her oath and she is willing to do the same. That's what you have done here:
http://i41.photobucket.com/albums/e288/JediShemL/Handmaiden%20Progress/HandD61.jpg)
http://i41.photobucket.com/albums/e288/JediShemL/Handmaiden%20Progress/HandD62.jpg) (
http://i41.photobucket.com/albums/e288/JediShemL/Handmaiden%20Progress/HandD61.jpg)
http://i41.photobucket.com/albums/e288/JediShemL/Handmaiden%20Progress/HandD63.jpg) (
http://i41.photobucket.com/albums/e288/JediShemL/Handmaiden%20Progress/HandD61.jpg)
The influence gain is in the line "And you are important to me, more than you know. I will accept..." (E184). You have to go through that conversation eventually because that line sets the global 000_Hand_Dad_Teach. The influence gain itself, on the other hand, isn't important. If you had enough influence to unlock this line then you wouldn't need any more to make Handmaiden a Dark Jedi either: The influence checks you have to pass before jedifying her are in E187 and E148. Both say you must have >74 or <26 to get the Influence: Success lines. That means you need 82 to train her. Correct me if there is a dialog node that requires higher influence.
You'd end up with 98 influence, not counting the final gain from E184 after the third sparring match since it is irrelavant. So far, all of this is done in Achilles' walkthrough as well.
The walkthrough takes Visas' Arrival into account which you must do. You either have to take a LSP hit or loose influence. If you take the influence loss, you have 90 now. Still enough to train her.
Following the walkthrough you get 8 more influence by asking the Handmaiden about Atris.
Again with the mysterious 16. As with the first example, I'm not sure where that 2nd bump comes from, but I'll give you the benefit of the doubt and assume that you're referencing the boost you get when Handmaiden renounces Atris. Fair enough?
Well here's the rub: You only get the other 8 points if you have >90.I don't think that's correct. Take a look at the condition of E187: You need >74 or <26.