restricting open ringing it sounds like an unfortunate situation, and maybe there are undertones that limit what can or should be done. But from the information given my thoughts are:
1. I assume the complaints about sound in the churchyard come from people living next yo it, not from those interred there.
2. How serious are the complaints? Was it an isolated one off moan from a one off situation or is it a real hardship in a recurring situation?
3. Could you improve the synthetic sound, for example better speakers, different pitch or a different audio file?
4. If you can get hold of a sound meter it would be worth measuring the sound levels at various points with and without the sound control shutters closed. 20dB difference is fairly effective.
5. Are the shutters significantly less effective on some sides than others? If so are the closing properly, and check for a poor fit or missing seals.