If you honestly believed you smacked or broke the HD heads, then that h/w will preclude any saving of data and destroy further any "self-recovery" of data, no matter what method. You may get lucky and get something but also making sure the remaining data becomes even harder to recover. Real damage is only going to get worse and further, the recovery service of some co. uses other methods available to it for retrieving that data may not work as well or take longer. Data recovery service can only do so much but they have the full range of potential recovery tools. The service will still try a full retrieval of data even what you already done yourself, that's what you're paying for.
FYI- Now consider all the hassle you're doing now and use that as a learning experience to take the time and effort it takes to save your data and/or burn to CD/DVD/BD discs in the future of at least the super critical data before the major back-up or retrieval process.