Here it all depends on how [b]Important[/b] the Data on it is.
If it's [b]Important/Vital[/b] to recover it I wouldn't bother messing around with it just pack it up and send it off. The more that you do now unsuccessfully the more that it's going to cost to recover the data and the greater the chance that it will make some data impossible to recover with methods that are Affordable.
Of course if you know someone who works In Forensic Recovery for Legal Authorities like those who are given drives and told to see what they can get off them for Court Cases like Kiddy Porn or Treason and the like they can read every layer of data that was ever written to the drive but I believe that this is beyond the price range of normal people. I have no idea of what the costs are but I believe that are not cheap as I know what is involved. However if you have someone working in a place like this they often take in Drives from friends to do Practice Runs or confirm the function of the equipment and do it for free as the costs are incorporated into the Court Recoveries and are part of what is required to keep Certified.
But with the drive causing the system to hang this very much sounds like a serious Hardware failure so the chances of making things worse are greater and getting noting back is highly possible for affordable Recoveries.
With all Data Recovery ways of doing things you should save the Recovered data to different media so you read off the [b]Problem Drive[/b] and save to something else. You never write anything to the Affected drive as this runs the risk of Overwriting data.
But just as a thought here have you tried a different Power Supply? If the one you have is on it's way out or underpowered the Hanging/Freezing problems may be nothing more than not enough Power being available.
I personally prefer Antec Power Supplies because their Rated Output is for 100% of the time where as a lot of Cheap No Name PS's are rated to a Peek Value like HiFi Ratings. They can provide that Power Output for short periods of time and then fall back to something considerably less. ;)
As you already have the steps to proceed here which Data Recovery Company you chose is up to you I however prefer On Track but I have dealt with them on numerous occasions so I'm probably Biased. ;)
I just find if you stick with the best you get very good service but you however need to realize that there are limits involved as to what is possible within a Money Limit that the Recovery Companies.
After all you don't want them to rush head long into a 1 Million $ + recovery and then have to find the money to pay them. ;)
Col