The thing with the frame rates does sound a bit strange -- especially that 119.88 fps one with tmpgenc. As you will probably have realised, that is twice the progessive NTSC frame rate of 59.94 fps. I cannot think why it would double that -- unless it read the original as being an interlaced frame rate and doubled it to give you a progressive rate...
The downward conversion to 29.97 (half of 59.94) is perhaps a little more obvious and that has to do with the other problem i.e. the conversion to mpg instead of .m2ts/.mts. And I think that in turn is linked to your use of Share > Create Video File > Same as First Clip.
First, though, can you right click on the wonky .mpg file you produced. Do this inside Video Studio -- either in the library window or in the timeline. And copy down ALL its properties here please. Then we will know exactly what we are talking about.
At the moment, I have two theories. One is that you are converting the file to HDV 720p, and not AVCHD. That can use the mpg extension. But I am not sure how it would happen, unless by saying 'same as first clip', VS saw 720p, looked through its database, and only found a HDV template which used 720p. That could have screwed things up.
The other possibility relates to the fact that I don't think 'same as first clip' works with high definition video. It certainly does not with my HDV. Instead, you have to actually choose one of the high definition outputs specifically. However, as you may already have found, there is no AVCHD output in VS for 720p -- the only one being HDV, as I already mentioned above. So what I think could be occurring here is that VS gets the command Share > Create Video File > Same as first clip, but cannot actually "see" the high definition properties of the first clip at that point. And so it uses the default project properties which, I think you will find, are standard definition mpeg-2 -- which of course also uses the mpg extension. And standard definition video for a DVD has to be interlaced, so that would account for the interlaced NTSC frame rate of 29.97. That could also account for the low quality result you have been getting -- though it does not explain the strange frame rate business with tmpgenc...
As for whether loading the installation disc might give you the correct codec, it's just a 'maybe'. It depends on whether VS can "see" it and thus use it instead of its own AVCHD codec which, as far as I am aware, does not deal with 720p AVCHD...
One other thing you might want to try to get around that 'same as first clip' business is to make a template using one of your captured original clips. In VS, go to Tools > Make Movie Template Manager. In the dialogue box which appears, click the Add button. In the new dialogue box which appears, give the new template a name (e.g. AVCHD Lite). In the little window above that, which says mysterious 'File path', click on the button to its right which only has '...' on it, and navigate to where one of your original files are stored, and select it. Then click OK to get out of all that and back to the VS main screen. Now when you click on Share > Create Video File, at the very bottom of the drop down menu which appears, there should be a new entry: AVCHD Lite. So next time, when you finish you project, choose that instead of 'Same as first clip'.
(NOTE: do NOT try to change the settings within this new template. That simply causes it to collapse into a standard definition template, and you have to start all over again.)
With the new AVCHD Lite video file you produce, you can down-convert it to standard definition video. Note here that your original video is progressive scan, but a DVD must be interlaced. So it will end up with a frame rate of 29.97 fps. I would use Upper Field First because that is the Field Order used by all interlaced high definition video, both HDV and AVCHD. If you in fact, in your experiment to date, used a default template, I would guess that it uses Lower Field First, which again could account for some of the low quality results your received.
Another possibility is to use Share > Create Video File > AVCHD. This should at least keep it as AVCHD, albeit with a larger frame size. I would choose the 1440 option as it is closer to your original frame size of 1280 x 720, and uses a bitrate of 15 Mbps which I assume is also closer to your original bitrate (12 Mbps?)
Looking forward to hearing back from you!!
