I'd like to chime in about this situation (not having a lot of options to get experience in a given setting). As a TD I understand that there may be limited options for trainees to get the experiences they want. What makes a difference for me when I review an application is how the person communicates their interest in and passion for working with the population at our site. If a letter just says, "I think I would be a great asset to your program because I am excellent at all these skills," that does nothing to convey genuine interest in our site and the people we serve. What I appreciate seeing is "I haven't been able to do X, though it is my long-term career goal. These are the A, B and C ways in which I have prepared myself for work at your site/with the people you serve, and these 1, 2, 3 reasons are why I will do well there." Or something to that effect. Don't count yourself out. But do convey your interest and passion.
Good luck! I know this is hard.