The post is already a few days old and might have been solved already. We go often to Ban Laem and we know the procedure there, but something in Op story not add up. There is no reason why the IO would refuse you to exit. You got old passport, new passport and Letter, that is all they need to transfer. On the Cambodian side they put visa in your new passport and let you stamp in n out of Cambodia, then you head back to Thai side. Straight procedure. I only aware that for some tiny country like Maldives the Cambodians have refused the visa, because they have never seen the red Maldive passport.