$1K to "find and fix" the leak??? It's time to find a shop that will charge a reasonable rate and do the work right. A good shop will charge the system and insert a dye to find the leak. Once that is done and the leak found, then an accurate estimate of repairs can be provided to you.
Simply tossing in more refrigerant does not solve the problem. As mentioned, if the system is completely empty, a vacuum will have to be established to get the system to even accept refrigerant.
Find a good shop and have it done right so you can avoid the same problems next time.