I like your conclusion a lot, but I think your premise may be a bit off. I was always under the impression that Luffy's power draining was in reference to how he gets after using Gear 4th; in Dressrosa, using it sealed off his haki for about ten minutes afterward, and this scene seemed similar. That said, I can't disprove your point, cus Big Mom did have an aura around her hand and the transition from Gear 4th to being drained was very sudden, so maybe it was a misdirection to make people like me think it was just Gear 4th timing out. Either way, I think your overall interpretation was right, that the flame-patterned haki combines the user's Devil Fruit ability with their haki, and that does seem like the most likely usage for Big Mom's Soul-Soul Fruit.
