I always write a cover letter with my rental applications... Not sure if you have done this already but I think when a real estate agent has 30 or so applications to go through you need to stand out in some way or another.. In my letters I usually write is like a mini bio/cv e.g. this is what me and my husband do for work we have a daughter named blah and she is blah years old - we have a dog named blah blah we have lived in the area our whole lives and are looking for a long term rental etc etc.. It just helps them get to know you a little bit better and make a personal connection with you..
I have rented and always had really good responses from my applications..
I really hope you find something soon! It can be really stressful