If the Closed Captions work correctly when you playback the original recording in MC, then I would focus on the transcoding and CCExtractor.
I would definitely increase the pre-padding to get a more stable signal for the actual program. Give the tuner more time.
You haven't said what you use for the transcode, or if you extract CC from the TS file before transcoding, or from the transcoded file after transcoding.
If using MC to transcode, which has issues in terms of the audio produced always being stereo, then I would set the Playback Range for the file before transcoding, so that it only includes the program, and would most likely get the audio and Closed Caption synchronisation correct. Besides, once you have the Closed Captions in SRT Subtitle form, MC can adjust there timing in 100 millisecond steps. So unless the video is stretched or compressed in the timeline by the transcoding function, you should be able to get them aligned correctly and they should stay aligned for the duration of the program.
I'm sorry but I think you have requested a solution that doesn't address the problem. To test that theory, try this simple process.
Pick a program that is going to be recorded, and which will have CC and you will want to archive.
Start playback of the TV channel live five minutes before MC is due to start recording, allowing for the pre-padding.
Process the resulting recording exactly as you do now.
Did that fix the issue? It should have, if your requested solution was going to work, because all you did was manually warm up the tuner and get it stabilised on the channel before starting the recording, just as per your request.
Of course, I'm sure the issue happens to greater and lesser degrees with different programs, so repeat the above test a few times to be sure that it does, in fact, eliminate the problem. One test that works is not the basis of a reasonable conclusion.