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Thanks for your patience and enquiry. It is likely you were turned away because they formed the view that if you were admitted into the country you would not leave.
The K1 visa is a good option. This allows you to enter the US as a fiancé, get married and then apply to stay in the US. He needs to be in the US when you apply for this visa though.
Can I clarify anything for you? I hope I have answered your query in a way that is simple and easy to understand. If anything remains unclear, I will be more than happy to clarify it for you. In the meantime, thank you once again for using our services.
It is likely that the refusal will be on your record. You would only need to explain the circumstances surrounding the refusal of entry when you apply for the k1 visa. You are unlikely to be prejudiced by this.
I do believe your proposed route is the best one.