FCE Jumpy Transitions on Exported HD Product Only

Hello everyone. I am normally a forum-stalker who never contributes but I have spent a significant amount of time unsuccessfully researching this problem.

I just purchased a GoPro Hero 3 camera and filmed under the 720 30fps setting. I imported several clips to my laptop and proceeded to open FCE 4.0.1 which I have been using for a few years. I mistakenly did NOT change any of the settings under Easy Setup before spending quite a while editing my first HD video ever. I was also editing using H.264 m4ps. I know. After an embarassing amount of rendering, I exported the clip and realized that while the editing turned out great, it was set to 720 x 480 the whole time and the quality was not what I was looking forward to.

After complaining extensively to my wife, who politely nodded while completely ignoring me, I eventually sat down to re-edit the whole clip. First I used MPEG Streamclip to convert all the files to AIC coded .mov files. Then I imported the clips and compared all of the item properties of the clips (1280x720, 29.97 fps, AIC) with those of the sequence (the same). I then begrudgingly remade my lovely Christmas video all over again, cut by cut. I needed to do significanly less rendering, which was lovely, but still rendered all the green lines away before watching the whole video in the canvas. It looked perfect. I then exported it, self-contained QuickTime Movie. I finally had my first HD video, but then I watched it. All of the transitions (and only the transitions) are terrible: the clips zoom in and out abruptly during all of the fade-in/outs as well as the cross-dissolves. The brightness and saturation changes as well, blatantly noticeable flickers, just during the transitions. I uploaded an example to https://vimeo.com/56495362. That's a random part of one of the clips I was using, first cutting from one clip to another with no transition (seemlessly) then a copy of the same two clips with a (laughable) cross-dissolve in between. It's not hard to see what I'm talking about.

I have tried to search to the ends of the internet. 90% of the problems people report with transitions are solved by using longer handles. I assure you this is not the case. 9% seem to be solved by rendering before exporting, also not a problem. The remaining 1% seem to be cured with a quick deletion of Final Cut Express preferences, which I also attempted unsuccessfully. That covers 100% of the transition problems that I have been able to find on the forums. I even gave up and tried resetting my computer. No luck.

As a test, I went back to my original (standard definition) product, changed the sequence settings to AIC 720 30fps and re-exported it. Though all of the aspect ratios were warped, the transitions were fine. Then I added another clip at the end of that original sequence, with a transition, and that transition was messed up.

Basically, if the sequence settings and the clip settings don't match, the transitions are great but the aspect ratio or the zoom is messed up. If they do match, the video is beautiful - as long as there are no transitions. Please help.

Surely I am missing something relatively obvious?