Final Cut Pro X :: Controlling Output Video Bitrate

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. 

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... 

Info:
iMac, OS X Mavericks (10.9.4), FCP X - Canon HF M56 PAL