Where I work, we have a different problem, but one that affects our morale nonetheless. We are being Low-Census'ed to DEATH. I think it might take your nightshift staff uniting, and making it a point to go knocking on your nurse manager's door w/ your concerns. What we have done is to actually get in touch with our DON since nothing seems to be able to be accomplished on our unit to change things. One of our biggest concerns is the day shift is losing roughly 1/3 to 1/2 FEWER hours than the dayshift staff are. It's not a dayshift versus nightshift fight but a matter of fairness.
I realize this problem is a lot different than yours, but morale is a huge issue for us, and this is a situation we can't live with. People are burning up PTO (those that are lucky enough to have it; I don't) to get paid. And the worst is, it has been going on for MONTHS. Several of us have made application and set up interviews with other hospitals, not out of spite, but in order to take charge to change of an increaslingly unliveable situation. I actually love where I work but I need moolah, ya know?
Anyhow, We have made management AWARE of the fact that several of us are looking at leaving employment there. Even the doctors are concerned and involved and (I hear) talking to the CEO about this issue. They sure don't want to see 50% or greater of their experienced night shift leave.
Do what you have to do, but don't let this ride. Staff meetings getting canceled? Let them know you are making note of this and that your means to air out these things is being stymied. You may have to go higher up to get your concerns heard if you are being stonewalled at this level.
Get your coworkers together and knock on some doors, write some letters. Document what you are doing to try to change it and let them know you are doing this. You obviously have a HUGE legitimate concern that affects not only morale, but safety! I wish you good luck. Sorry I am not much more help, but I want you to know I support you as a fellow nurse nightshifter. Keep us up to date! I feel for ya!