Try to free up some wage budget early by offering the players you don't want to retain by offerring mutual terminations (they'll usually accept for free if they are in the last month of their contract). Getting them off the wage bill should mean the board allow you to offer more to the players...
When you offer people a role that is not their preferred role they are less likely to accept - but if you through enough money their way they may be tempted.
Don't worry too much about this, it is just how lower league clubs survive. Increase revenue by increasing attendances (you can achieve this by winning games)/selling players/progressing in cup competitions. The board are unlikely to increase your budget if they regularly have to do this...
I suspect you're training your players too hard. Check the training section for individual players in your squad and look for their workload - I think your players will have a heavy workload. This can cause players morale to drop or worse, cause injury to be more likely. Reduce the amount of...