Hi,
I too came to the USA on a
K1 visa and unfortunately it took about 14 months from when we applied to me actually arriving here.
It is such a long and drawn out process - the longest wait was for the 'interview' at the American Embassy. Once they approved my application I then had to wait for my medical.
It does seem to take forever but all I can say is be patient! It will all be worth it in the end. There is no hurrying along US Immigration. They go at their own pace and although it is frustrating for you, there is nothing you can do about it.
It sounds like you have a pretty straight forward case and that it will be approved eventually.