Sorry to hear about all the stress. I would say to move on and find a new tenant.
If you insisted they pay and move in per your lease, do you want to start a hopefully long working relationship like that? And how can you trust someone who doesn't honor their words to execute the lease and take care Of your property?
If you want to get loss in rent damage, how much did you really lose? I am feeling like this is far from an ideal tenant applicant and yet you decided to rent to them, which tells me perhaps you didn't get other interested parties. So I would reevaluate the pricing. It is perhaps priced too high. In reality, would you have rented it at this price to any body else if this trouble tenant didn't commit to the lease?
Third, I always take a non refundable holding deposit before I process any tenant applications. It is anywhere from $200-500, which means when I receive this in cash, money order or cashiers check, I will take the property off the market, and process the applicants application. If the application falls thru because of untimely or the lack of cooperation from the tenant, or any other wrong doing, I forfeit the holding deposit. If the application doesn't go through because of something out of their control, like job loss, or whatever, I return the deposit. If the application goes through, I apply that fee towards their deposit. That way, you can cover this exact situation.
Honestly, congratulations! You just had your first lesson as a landlord, and it only costed you one month rent. Many lessons can only be learned through making mistakes, and most mistakes are very expensive.