Songs registered with BMI will stay BMI. Your affiliation as a writer will change on your new stuff. YOu have to submit a formal letter apprising them of your intention to change but you have to wait until your contract date comes up. You should apprise ASCAP of your intention to switch.
I would not get too concerned with them not calling you back though. If you come to ASCAP, SESAC. PRS, etc. and do not have a lot of activity on songs, you are not going to get much attention from anyone. It is unfortunate but true. There are just not the man hours to do it.
With about 3 million writers at any one time, there is no physical way that they can respond to every one. They do try, but unless you make a face to face appointment, it is doubtful you will get much response. If they check your files and there are some significant activity money wise, they will respond to you.
It is one of the misunderstandings that people have about performance rights organizations. They feel that there is a huge universal agency that monitor every song played anywhere. There is no physical way to do that.
They monitor regions of airplay, catalogue airplays on major reporting stations, televisions and movies, and oversee activity on largely played songs.
ASCAP has an "Awards" program, that artists and writers can apply for each year in April and if you have smaller activity, college stations, performances in writer's shows, etc. you can get paid for some of those. Kind of a grant program.
If you can imagine having to go through five thousand e-mails and 300 phone calls a day from people from all over the world wanting to know how to collect money on songs played at a street festival in Bangor Maine, you get a sense of what they go through.
They are there as representatives for writers and do offer workshops, seminars, networking events, as well as lobby and interact with legislative bodies, and all facets of the entertainment industry. But there is only so much any organization can do and not all of us are always going to get the respect or help we feel we deserve.
Continue to try to contact a representative. But until you can really go there, you are going to probably get similar results.