I have a data recovery company, but we usually leave iPhones to others who specialize in that field. However I have a regular client who specifically wants me to recover an iPhone video. There is nothing wrong with the phone, the video was deleted about a month ago. He has used recovery software and has recovered about 20 deleted videos but not the one he wants. I presume if there is nothing wrong with the phone and he has got deleted files, then there is little chance of recovering this 'deleted' data as I would imagine its been over-written. Would a DR company with Cellebrite (or similar) be able to get more information from the phone?

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HDD, SSD, Flash and RAID Data Recovery
Founder of The Data Recovery Professionals Group

Very, very unlikely due to the time frame, and that the video was deleted and the phone was still in use. Chip off recovery for iphones after 4 is very painful. It is possible a tool could get more info, but I think this would be a miracle.