Asking for a specific bitrate on ProRes files seems to be rather odd. They specified ProRes 422HQ and that's what you have (assuming your resolution and frame rate match what they need). When making ProRes files, you don't specify bitrate. They are what they are and the bitrate can vary a bit. Nothing to be concerned with. I would not change your video before handing them off.... transcoding them would just result in a slight generation loss at this point and there is nothing to gain by increasing the bit rate.
Completely understood. The footage was shot around 5 years ago. Canon Cine Platform to outboard 10-bit recorders, per Netflix/Apple TV specs. Of course over five years the specs have changed and now they are Netflix/Apple requiring 442HQ HD with a bitrate ~ 220 Mbps in their QC protocol. The project has been 4-walled with DPC and from what I have seen, it looks fine.
I can export it out of Compressor as uncompressed 10-bit (or 8-bit) but the file size is over 500 GBs. But that is a bit obsessive.
They are saying 220 Mbps because that is the approximate bitrate of Prores 422HQ with 1080 frame size and 29.97 frame rate. This varies depending on the complexity of the video footage and other factors. I believe submitting what you have in 422 HQ will be acceptable. Here is Apple's current white paper on the Prores codec :