This may get down-votes since it's so manual and doesn't have perfect video quality, but I'll offer it anyway.
CREATING THE GENERIC TRANSITION
- Bring 30 clips into a project.
- Shrink the scale of all of them.
- Drag them onto the timeline so they're all playing at the same time.
- Position them in a grid.
- Export that project in the best possible quality you can.
CREATING THE SPECIFIC TRANSITION
- Open the generic transition video in a new project. Place it on the timeline.
- Bring in the 2 videos you want to transition between.
- Shrink their scales, put them on the timeline, and position them over 2 of the existing videos.
- Export that project in the best possibly quality (matching the generic clip).
USING THE SPECIFIC TRANSITION
- Import that specific transition into your project.
- At the end of the first clip, place the specific transition on the timeline.
- Animate the motion of the transition: Start with the scale zoomed in on the "starting" video. Scale back to 100% while moving the clip to center the "ending" video. Scale up (zoom in) on the "ending" video.
- When the "ending" video fills the screen, cut the specific transition.
- Add the actual "ending" video to the timeline. Trim the left end of the clip to match the right end (last frames) of the clip in the specific transition.
I haven't tried this but in my mind it should work really well. The video quality will be a bit lower during the transition, but it may not be noticeable - especially in lower-quality environments (like web video) or if the transition is brief (1-2 seconds).