As for the lease break clause check your local laws. It might not hold up.
I doubt you can take anything more than the security deposit. Caution, call it a “security deposit” not a “damage deposit”. Again check local rules. In my area a “damage deposit” can only be applied to damage, a “security deposit” can be applied to unpaid rent, damage etc.
I have been a LL in two different areas with very different rules. In one area you cannot penalize someone for breaking the lease.
You can take any missed rent out of the security deposit or go after them in court for more.
But you must prove that you have tried to rent the premises. If you get it rented the day after they leave there is no charge even though it was a major inconvenience for you & you had to pay for advertising, cleaning etc.
If you are trying to rent it but can't, or lose more than 1 month rent, then you can go after the tenant but I would be wary that a judge might say your place it too expensive, etc.
In the other area the renter is responsible to pay the rent in full until the end. They could technically be on the hook for thousands. So, in that area it is much more common for the renter to be rpoactive and assign the lease.