Has anyone ever used a program like that? I have not.
I have, and it sort-of worked.
What I'm wondering about - after you are told that the file has been recovered and you pay the price they request, do you actually get the file? And is it the file you were after?
The drive on which I used the tools (Data Rescue AND Disk Drill Pro) had been accidentally erased. I first did a sector by sector clone to an exact match drive so I had a backup. Then I used DR first. It spent a very long time (more than 20 hours) grinding away. It did not write the recovered files to the drive, but put them on a separate drive (yes, now we are at three drives involved), so that the original damaged drive would not be altered. At the end, I had a pile of files cleverly named "file00001.txt" through "filexxxxx.txt." No directory structure and no file types, just 500,000+ files named "file." I spent some time opening each one in turn to see what they might be. An awful lot of them were what I would call "work files" in that they showed just part of a file. For example I had several dozen versions of a jpg that I had edited in Preview. Each version showed just a part of the image. Top, middle, bottom, 1/3, 2/3, etc. Never did find the full image as I gave up looking on the drive. Tried Disk Drill Pro on the drive, went through the same process, got basically the same result. I still have the recovered files on that drive they got written to, but I don't have time to spend to go searching through 500,000+ files to see if anything is recoverable. So, do the recovery tools work? Depends on the definition of "work," and how badly damaged the drive may be. If all that has happened is that one file is erased, and if the drive is otherwise working, and if nothing has overwritten either the file or the directory space, then yes, you can recover, most likely. But if the drive is totally wiped, or the directory is totally damaged, then while they will "recover" something, it won't be useful and will require a LOT of time to piece back together into something usable.
For the OP, it may be recoverable, if the directory space is intact where the data on that file was kept and if the disk sectors where it was stored are still not written over. The longer the system is in use the less likely it will be. And to be careful, the OP should use some OTHER drive to download the tool, install it there and run it from that place to the drive where the file was. Otherwise, the simple download and install of the tool may overwrite the very data that needs to be recovered. If it's on the internal boot drive, that may well mean using a separate system and target disk mode, if the tool supports it.