FWIW, FCP can export as mp4.
You can use File->Share->Export File and then under Settings, choose "Computer".
The data rate will probably be too high for what you need, though.
Alternatively, you can also export for "Apple Devices" and then manually change the file extension from .m4v to .mp4
As to how much you can compress the file, I noticed that you have another thread on this. You never mentioned what type of content this is; also, quite importantly: you seem to be using "Send to Compressor".
Try exporting a ProRes or H264 file straight from FCP, and then bring that file into Compressor.
In my experience, there can be issues, and limitations, with Send to Compressor.
The overall time may actually be less if you do it this way, too (this may depend on which mac you have).
Compressing an actual video file, rather than a project from FCP, can use all available cores with multiple Compressor "instances".