I wager, in fact, that the poor woman has become Didyme for all intents and purposes

If she has, that might imply that Elspeth's power doesn't just send memories/experiences, but also personality traits. Or that identifying strongly with a set of absorbed memories is enough to give you those personality traits (I don't really like that theory).

The bond might or might not be affected by personality, but I'm not sure I could consider her to be "Didyme resurrected in a new body" (or even just "close enough") unless the personality was basically Didyme's (or close enough).