I find it easier to use SUP files than SRT files for subtitles. I'd use the 720p SUP files from Project Threepio (not included in the Project Threepio folder that came with the MKV, but available on MySpleen). Just add that as a stream just as you'd add an audio track, and be sure to label it with the appropriate language.

Theoretically, I suppose you could still use the SRT file with tsMuxerGUI, but I've never tried that so I don't know if it will work, or how to troubleshoot it.

As for "showing up", that could just be a matter of software. If you play it in an actual hardware player, subtitles should work if they're present. MPC-HC shows HD subtitles, but helpfully not under the subtitles menu, but under the filters menu. VLC recently added HD subtitle support so there may still be bugs. Depending on how you were playing it back, your AVCHD may have been fine all along.

EDIT: Oh yeah, keep in mind that the English subs are timed to the English dialogue, so they may show early/late for the Japanese dialogue.