Do you already own the land? If so is it free and clear or how much do you owe and what is as is value?
I understand loan amount and what the appraised value is but what amount are you acquiring the land for? - Additionally what is the cost to build and the after completion value?
Depending on how long you are projecting for development, you might look at a hard money lender for construction and then finance them out post-completion. With only a month until closing, bank financing will be tough. With more time, you should be able to find a more conventional lender to provide temp to perm financing which would cover construction (temp) and then convert to permanent financing upon stabilization.