How can I get a postdoctoral position in neuroscience after completing my PhD in Mechanical Engineering? I recently completed my PhD in mechanical engineering and have been applying for postdocs in neuroscience for the past 5 months.
My field is dynamical systems theory and statistics, so I look up professors working in neuroscience who use those techniques and send them emails.  I have sent 3 dozen emails since February but I barely get any responses.
I got two interview requests in February. One of them rejected me. The other professor stopped replying to my emails after the first interview and he did not pay my interview travelling expenses either.
Sometimes it feels very hopeless. Please, please any recommendations, help or advice is very appreciated; especially from people who have changed their research area post-PhD.
This is my Cover letter.

Hi Dr. F,
I am writing apply for the postdoctoral position in your lab at Columbia. My training is in the domain of dynamical and nonlinear systems theory (primarily in mechanical systems) and I am interested in bridging to Neuroscience for my postdoctoral research.
My interest in the brain goes back almost a decade to my undergraduate
years when I took up a regular meditation practice. I am very
interested in the broad and mechanistic aspects of neural computation.
I am fascinated by the application of concepts such as dynamical
systems, stochastic modelling and network theory to the study of the
brain.
I completed my PhD in Mechanical Engineering at the Some University
under the advisement of Dr. Advisor (June 2018
Conferral). I have worked on a wide variety of problems so far -
powering micro-implants in brain using arterial blood pressure,
stochastic analysis of nonlinear vibration energy harvesters, the
spontaneous spinning of a rattleback on a vibrating surface, sound
wave manipulation in fluids, tunable mechanical metamaterials and
nonlinear metamaterials. I currently have 3 published manuscripts, 2
journal papers in peer review and 1 manuscript in preparation. I have
published 9  peer-reviewed conference papers. During my PhD, I have
worked on collaborative research projects with senior faculty and also
as a mentor to several undergraduate students. I previously earned a
Bachelors and Masters in Aerospace Engineering from Indian Institute
of Technology (IIT), Kharagpur (Class of 2013).
I am fascinated by &gt; your recent research contributions. I really liked the paper titled &quot;  Abstract Context Representations in Primate Amygdala and Prefrontal &gt;Cortex&quot; that used neural population decoders to show that
representations of task contexts appeared in the Amygdala in addition
to the PFC. Also intriguing was the preferential weakening of the
signal in the Amygdala when an error was committed.  I also liked you
paper titled &quot;Energy efficient Neuromorphic classifiers&quot; that
implemented a basic image classifier on a novel neuromorphic processor
and demonstrated significantly lesser energy and computational cost.
During my postdoc, I intend to apply for fellowships and possible
avenues of funding. I am interested in using my training in dynamical
systems and stochastic analysis to current research problems in
neuroscience and hone my technical skill-set to succeed in my future
independent research. My CV is attached. Please do not hesitate to
reach out to me for further inquiries.
I have the same issue, I recently completed my Ph.D. in computer science. Accordingly, I have applied several times for post-doc positions around the world and I was able to get only three interviews. Unfortunately, none of them was willing to give me the post-doc position. 

Based on my short experience, it will be better to submit your application for a Fellowship with peer review process such as Marie Skłodowska-Curie programme. Open up to the world (China!).

Best wishes.