I have to admit that I have never seen American Idol (must be the only person, who has not?), but from your description, this might work for you:
Find, or create an abstract blue background Video. I know that there are sources for "stock motion footage," and I have created similar in a few NLE programs. Set the Duration fairly short, and place your logo w/ Transparency on the Video Track above this footage. Adjust Opacity, etc. and then animate the logo with the fixed Effect>Motion>Position. Use this as your "transitional" footage, and just add a Cross-dissolve between your Clips one either side of this "transition."
I'd do this compositing on a separate Sequence, and when complete, just Export, then Import into the Project, and use it like a stock image.
One could do this with Nesting of Sequences, or could do the compositing completely in AE for Export/Import, or Dynamic Link. Personally, I'd do it in PrPro, and just Export that Sequence and Import it for use in my other Sequences.
Here is one possible SOURCE for stock motion backgrounds. Might be something useful there.
I just looked at Muvipix, and found about a half-dozen stock motion Assets, that appeared promising. Some are free with just a sign-up, and some are either available for purchase, or free with a subscription.
A few of these looked like they would work fine. I'd probably adjust the Brightness and the Contrast (several possible Effects for this), and probably do a Blur, maybe even animating the degree of Blur a bit.
Depending on your logo, you might want to do some simple 3D animation, with maybe Motion>Position and Motion>Rotation.
Remember, you will want your logo to be in a format that supports Transparency, like PSD, PNG, or even GIF (do not like that one personally). If you have the logo in AI, I would definitely use PS to Rasterize that to .PSD with necessary Transparency, and Scale it in PS to suit my needs.
Let us know if this helps, and if it's close to what you want to do.
You rock! Thanks again for helping me! I really appreciate your time and help. Hopfully it won't be long before I can answer some questions for others.
Just looked at my bookmarks on motion background sources. Three of those are now dead, but I found two others, besides the previously mentioned Muvipix.
Here those are:Hope that this helps,Hunt
No problem. That is how I started here years ago - asking questions like yours.
Maybe I need to catch American Idol to see exactly what you are looking for. Still, I think that you described it well enough to give me some ideas.
One of the programs that I have used for similar is Magix Music Maker and their "stock images," in their SoundPools collections These are in a proprietary format, but are the visual equivalent to music loops (Loopology). I have used those and then taken them into Magix MovieEdit Pro (it accepts that proprietary format), and done tweaking on the background motion pieces, Exporting to DV-AVI Type II files for use in PrPro.