Indeed, it is not that easy at all, and I never said it would be a piece of cake.I find it highly uncommon (almost impossible) to get recommendation letters from someone you have never interacted with before, no matter if you send them your theory/project, and how good it may sound.
In 1994 I tried to go to the USA as a graduate student in order to fulfil my research program (or project) and I needed three RLs urgently. I found three people who agreed to read my publications and discuss my results and my project. (Of course, I contacted more people but not everybody was ready to do this.) And all the three gave positive responses - they discussed my results with me and wrote the RLs. One of them, a Doctor of Mathematics from the Moscow State University, was the most strict: he pointed out that my way of presenting the results is of physical rather than mathematical level of rigour and asked me to prove that my new perturbation series converge in a regular sense. And one Physics and Mathematics Doctor from Moscow Lebedev's Physical Institute (ФИАН, LPI) got so excited with my result in atomic physics that I had to calm him down in order to obtain a reasonable RL.
I was not accepted to graduate programs in the US universities because nobody wanted me to work on my own project. Normally the graduate students work with their leaders on the leader's projects.
And today I am quite conscious about a low probability of any response from those who was mentioned in this thread.