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Scott, I don't think that RA changed to BC trips the trigger. The trigger is "Following" your rescue attempt. One event only follows another if it comes AFTER. For the shuffling to come AFTER your rescue attempt, your rescue attempt has to have finished. It's only finished after battle resolution. It is not finished just because a RA switches to a BC.
This REG entry made me think it worked:Battles where special abilities are triggered by the “end of a rescue attempt” only need to have been a rescue attempt at some point in the battle.Re-reading that after Mike's responses, however, makes me think I misinterpreted it. I don't see anything in the new or old REG specifically saying one way or the other, so either way, we need a decision/clarification.