Video/Audio Synchronization Problems after Trimming Clips in QuickTime

I often use the "Trim" and "Split Clip" feature in QuickTime to make simple edits to video files. I use this to quickly get rid of unwanted footage at the beginning and end of a video clip, or to split a clip into multiple files, without having to re-encode the video.

These videos play back exactly as expected in QuickTime Player itself, but the problem comes when I view them in other software.

In VLC, when I play back one of these videos, the video begins playing several frames -- maybe up to a second or two -- prior to where I had made the cut in QuickTime. The bigger issue is when I share the file with someone who uses Windows and they try to play it in Windows Media Player or Windows Movies & TV. There, not only does the video start prior to where I had made the cut, but the audio is no longer synchronized, but instead plays a second or two ahead of the video -- as if the audio is starting where I had indicated it should, but the video is delayed a bit due to the inclusion of those extra frames at the beginning.

Any ideas of what is causing this? Is this a bug in QuickTime? My instinct was to blame Windows Media Player for the de-synced audio, but obviously it is QuickTime that is including an extra second or so of the video I had cut out when it exports the file -- even though that extra footage doesn't show up it QuickTime itself. For what it's worth, the original files play fine in all three programs. It is only after trimming them in QuickTime and saving those trimmed files that these problems appear.

Also, any suggestions on how I can fix these exported files so they play correctly across all platforms? Unfortunately, I had edited many, many clips this way before realizing there was this compatibility issue...