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We got our CTC last week and are closing on Wed 10/14!! I did have to write a LOE and I really spent a lot of time working on that but after that was submitted, it was never brought up again as an issue. If they can see most of your's all revolve around the same short time period, I can't imagine them having an issue with it. I would plan on writing a LOE still but the UW should be able to connect the dots.
Good luck!!