It was not paranoia about Muslims. It was you telling them that you have a girlfriend in the US and then trying to correct yourself and hide the fact that you have a girlfriend in the US. I think it is very unlikely that your next attempt will be successful.
For any kind of family visa (K-1 or CR-1), you will have to meet in person. Plus, it would probably be a good idea anyway to spend some time in person with the one who you think you want to marry. That meeting does not have to happen in the US; she can travel to you or you can meet in a third country. Without meeting in person, there is no chance to get a K-1 or CR-1 (there are some very rare exceptions to this, but being broke isn't one of them).
You could explore other visa options, like employment or student visas.