Handbrake - by far
Handbrake is what you want. Free and awesome. You can get the significantly better daily builds at https://build.handbrake.fr I'm pretty sure you can use the High Profile preset and that it will play on the newer Sonys. I would do some test encodings with just a few minutes of video. Handbrake can also handle the 1080/60p video the TM700k puts out at the highest setting.
If you are on a Mac, you can also try ClipWrap (free demo for 1min of material, $50 for full version) which will just rewrap the mts files into MPEG4 containers without any video transcoding. Would suggest a good 801.11n router for that option.