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Firms have different policies for reconsidering applications post-AC rejection. I know some that have absolutely no issue with it and I know others that will not do it under any circumstances. If you were told the firm has no policy against it, I think it is worth a shot. Perhaps it will be somewhat of an upclimb because of the prior rejection, but you also know that the firm has liked you enough before to progress you out of a huge pool, so I think overall the odds are worth it. I also have heard of several candidates who secured a TC with a firm after they were rejected post AC in the previous cycle, so it is not a very uncommon situation.As for your second question, I am quite confident it is ok to keep your fundamental motivations unchanged; but try to (i) add insights into them and update the factual points about the firm with the newest information you can gather; and (ii) look as to how you can improve your writing and articulate those themes in a more clear manner.
Firms have different policies for reconsidering applications post-AC rejection. I know some that have absolutely no issue with it and I know others that will not do it under any circumstances. If you were told the firm has no policy against it, I think it is worth a shot. Perhaps it will be somewhat of an upclimb because of the prior rejection, but you also know that the firm has liked you enough before to progress you out of a huge pool, so I think overall the odds are worth it. I also have heard of several candidates who secured a TC with a firm after they were rejected post AC in the previous cycle, so it is not a very uncommon situation.
As for your second question, I am quite confident it is ok to keep your fundamental motivations unchanged; but try to (i) add insights into them and update the factual points about the firm with the newest information you can gather; and (ii) look as to how you can improve your writing and articulate those themes in a more clear manner.
