Controlling output video bit rate in FCPX

Question

I ran into a problem: I created a mp4 file with Share/Export File… (settings: Computer, H.264 Faster Encode, 1920x1080 - edited from an HD camera): its video always freezes at a definite point when played on my BD Player connected to my HDTV through HDMI (audio instead continues on the frozen image).
It seem that the issue is a sudden video bit rate pick of almost 50 Mbps while its average is around 20-30 Mbps. It is not clear to me if this freeze is caused by the BD Player or by the HDTV not being able to handle such pick.
As a test I used Compressor to control the output bit rate (settings: average 20 Mbps and pick 25 Mbps) and this seems to fix the problem. To be more certain I should do more tests, but I'm confident I found a possible solution.
I'd like to know if there is a way in FCPX to control such picks (without using Compressor), either in the Share commands (but it seems to me that they don't provide enough setting controls) or in the timeline. By watching the Video Scopes I can see a quite strong signal in the area where the output file has the bit rate pick. But I don't know any way to have a measure useful to identify them before sharing and avoid a trial and error approach...
Piero
Below the critical point...

Answer 1

Tried to upload a PDF instead of PNG, but no luck. The picture shows a quite standard (I'd say...) image but with highly dense graphic of Y' component in the Y'CbCr Parade (in the limits of 0-100 IRE): much more dense than most images in the rest of the movie. So I assume this might mean a higher bit rate... but it's just an assumption.
Let me summarize my tests:
1st test: FCPX: Share/Export File.. (settings: Computer, H.264 Faster Encode, 1920x1080)
- copied the .mp4 file to USB drive
- USB drive into a BD player connected to HDTV through HDMI >> freezing effect
2nd test: FCPX: Send to Compressor - Compressor: Create Blu-Ray Disk (on Hard Drive) and Video Job with standard Video settings (Automatically select bit rates = ON)
- Played the .img disk with "Mac Blu-Ray Player" on my iMac >> same freezing effect in same position as before on HDTV
3rd test: FCPX: Send to Compressor - Compressor: Create Blu-Ray Disk (on Hard Drive) and Video Job with customized Video settings: Automatically select bit rates = OFF - Average = 20 Mbps - Maximum = 25 Mbps
- Played the .img disk with "Mac Blu-Ray Player" on my iMac >> NO MORE freezing effect (and smaller file by 30%)
I might do more tests (mainly on my HDTV) but I believe the point is the bit rate... and the only way to control it is by using Compressor.
So now my question: is there a color setting that helps in controlling such situation ? e.g. lower saturation, or lower exposure, maybe in mid tones or highlights, or what ?
Thanks so much for your help
Piero