Why is the audio outrunning the video?

Question

First off, I'd like to say thanks to the gentlemen who helped with my last question; you guys lead me to the information that allowed me to figure out what was wrong and how to fix it.  I now have a new problem that's making me tear my hair out, and I'm hoping you guys can help me with this one as well. 
Background:
I'm attempting to make a video resume to supplement my paper resume in order to get a job with a technology educator called Techshop.  I have an old video production degree, but I'm new to digital editing.  For equipment I have a reasonably powerful computer (it exceeded the specs), a Panasonic HC-V10 camera (it records in ACVHD lite 720 60p, I think), Premier Elements 10, and a file viewer and converter called Wondershare Video Converter Platinum. 
My troubles all started when I, in my beginner's ignorance, didn't use Premier to capture the video clips off my camera directly, but instead took the SD card out and transfered the files onto my computer's hard drive directly.  I no longer have the video on the SD card, all I have is the files.  There is too much video to re-shoot; I need to use this footage. 
I set up my project as ACVHD lite 720 60p and, again not understanding what I was doing, washed all the raw footage through the video converter.  This was to get the resolution of the video up to 1280X720 from 960X540 and to label the video instead of just having numerical codes (pre-sorting).  I was changing the resolution because I couldn't find a Premiere preset for that resolution.  I converted the audio at 48 MhZ (after initially converting at a sample rate of 44.1, which seemed to cause a problem-though in hindsight, it may not have), which is the same as my project preset.
After converting the footage, it appeared to play perfectly in Wondershare.  I looked at the footage with MediaInfo, and it appeared to match my video presets exactly.  I used Get Media to pull the files into Premiere, and that's when it hit the fan.  The audio was outracing the video!  At the start of the clip it appeared to be in synch.  A few seconds in, and there was 'something funny going on'.  A minute in and it was badly out of synch, and a few minutes into a clip (several takes in one clip) it was so badly out of synch I couldn't even match the sections up.  The audio ended before the video in every clip I imported.  I'm not sure, but I think it's losing about 2 seconds a minute.  I also tried a test export, and the problem was exactly the same.
Now here's the interesting wrinkle.  When I look at the Properties of the clips in Wondershare and MediaInfo, they both tell me the frame rate is 29.97 fps and the audio is sampled at 48MhZ.  However, when I look at the Properties of the same clip in Premiere, it says the audio sample rate was 48MhZ, but the frame rate is 29.00!  If I'm calculating this correctly (though I'm not certain I am), I think losing .97 frames per second accounts for the audio/video missmatch-the video is playing slightly slower than the audio.
As an afterthought, when I Get Media the files into my Premiere project, I get a tiny message at the bottom of the screen that says Premiere is Conforming each video with a progress bar, leading me to believe that the project presets do NOT match the source video; only problem is, Wondershare and MediaInfo say it does!
Question:
What is happening?  How come Premiere is saying that these files have a framerate of 29.00 fps when everything else says they're 29.97?  Did I convert it oddly?  I checked, and I set the frame rate on Wondershare to 29.97 (which is what it and MediaInfo both say the video is playing at).  I even re-converted some of the video from the raw source with Wondershare at at 29.00 setting, and it STILL has the missmatch problem.  Did Premiere interpret it strangely?  If so, any idea why?  It doesn't appear to need to Render-there's no red bar above my project or anything.
Also, is there a way I can tell Premiere to play the video back with the same audio rate, but at 29.97 fps instead of the 29.00 fps it says it's using?  Or stipulate that the video files be played at the correct rate, or something?  Or really, any other ideas on how to address this issue?  Uncoupling the video and audio and then time-stretching seems very imprecise and cumbersome, so I'd rather not try it.  I'd like to simply adjust Premiere to use the video correctly, since my video is already labeled and correctly sized (and some of it is cropped and color corrected too). 
Edit: I just loaded in the unconverted footage for kicks, and the audio problem doesn't seem to be occuring.  Simple fix, right?  Well...I'd like to still figure out what's going on for future projects.  I also would like to still use the converted and labeled video since I took SO LONG pre-sorting it!  Lastly, I had at one point attempted to load all the unconverted footage into Premiere and just re-label there, but Premiere spat up a message that it was "running low on system resources" and soon locked up/stopped responding.  My computer doesn't seem to be able to handle 135 video clips in one project, and thus my need to pre-sort.  Just wondering, but is it the preview images that are the problem?  If I chop up the footage into multiple folders, will that help?
I have already read the articles by Bill Hunt and others about "File format as a wrapper" and "What's in a Codec" and such-VERY informative!-so no need to point me to one of them unless I've clearly forgotten something. 
Gentlemen, I thank you in advance for your advice and assistance, and I am very appreciative that you make your experience available to new users such as myself.  Thanks again!

Answer 1

I don't know why the audio sync problem is happening but I can offer a workaround that has helped me salvage files that were not able to be reshot.  The common denominator for the audio sync problems I have encountered in (some, not all) clips were 60fps.  It has been a while since I had to do this so please bear with me as I am doing this from memory.  Also, this is based on PE10 but will probably work with older versions but I don't own any.
1.  Right click the clip in your timeline and select "Unlink Audio and Video"
2.  Click any other place on your timeline to de-select the problematic clip and then click on the AUDIO portion to only select it.  To confirm that you did it correctly only the audio portion of the clip will be highlighted.
3.  Right click on the highlighted auido clip and select "Time Stretch...".  A small box will pop up with 4 adjustments - Speed, Duration, Reverse Speed and Maintain Audio Pitch.  Here is where the trial and error begins.
4.  If I recall, I used a few different methods to determine how much to stretch the audio to get things right.
                          a) You could determine how much time there is between the audio finishing and the video finishing by subtracting the values in the timeline counter.  Remember the last two numbers are frames and not fractions of a second.  Now add that value to the "Duration" value in the second line down in the open box.  It should get you pretty close to back to normal sync. If not good enough you can tweak the duration to get it right.  Next, check the box to "Maintain Audio Pitch" or you will sound funny.  If the pitch sounds funny you could add the "PitchShifter" effect from the audio effects toolbox though I have not had to this.
                         b)  You could click into the speed % box and enter an amount up to two decimal places in value.  Based on the fact that mediainfo says the clip is 29.00 fps (for whatever reason) I would try (29.00/29.97=.9676 X 100 =) 96.76% and see what happens.  Check the ' Maintain the Audio Pitch" box as above.  If this works then it may serve as a confirmation that Elements is indeed incorrectly interpreting the clips properties.
                         c)  Run and Gun.  Just start changing duration values or Speed percentages until you get it right.  Ya know, caveman style.
Another way that is possible I'm guessing is to click and drag the audio into sync.  Do steps 1 and 2 above.  Expand the timeline to show the waveform better.  Hover your cursor over the right side of the audio clip until the backwards "C" shows up.  Click and drag the clip to the right using the waveform as a visual reference.  I have not done it this way but in theory it should work.
When you get everything the way you want it you can trim off the audio portion that overruns the video to make them the same physical size.  Then hold the shift key down while selecting both the audio and video portions of the clip.  Be sure they are both highlighted.  Right click on the clips and select "Link Audio and Video" to relink the clips. 
Hope this helps you.  It is not ideal by any standard but what workaround ever is.  Good luck.