Q:"If we put together a slide show, the pictures of which are in no way synchronized with the recording snippets, and are "untimed" (no relation to the music being heard), why would a synchronization license be required?"
A: Wrong, they are synchronized. Random synchronization is still synchronization. If you are playing music in an audiovisual presentation, you are synchronizing even if you synchronize differently on different occasions.
You may want to hire a copyright attorney and discuss 17 USC 107 if you are an educational non-profit. I take it you are not, hence the need for the license since the use is not for the purpose of education (say if you changed the words to put in an educational message) but rather to raise money
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
ASCAP calls the license a synchronization license, it is the name of the license. That name is not confined to the dictionary term synchronization. If they say this is the license you need to buy for your intended purpose, that is what you need to buy.
If ASCAP and YouTube struck a license deal, that would be between them and it is unlikely to be public record.
You would be best served by consulting with an attorney in your area that is familiar with ASCAP licensing.
I agree with the other responses and would only add that your question suggests that you should consult a lawyer in private to make sure you are handling this correctly if you are uncertain.
Most of us here, including myself, offer a free phone consult.
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You will need a synchronization license. And ASCAP cannot give you this license. ASCAP represents composers and their publishers and collects license fees for public performances in live shows, concerts, and broadcasts (radio, television, cable TV, internet, You Tube etc). ASCAP does not provide, and has no authority to provide, synchronization licenses for use of a song in connection with visuals or slides on a web-site (the difference between timed and un-timed is irrelevant). You would need to obtain a license directly from the copyright owner. Also, it would be illegal for you to post a video of these songs or your concerts on You Tube without obtaining a license from the copyright owners (although You Tube has agreements with many of the major music publishers pursuant to which You Tube pays annual fees to some major publishers in exchange for rights to allow users to post music video "covers" tracks---but just because the publishers won't sue you, this does not mean that the copyright owners will not sue---the publishers often are not the copyright owners). You obviously have some rather significant misunderstandings concerning copyright law, and you need to retain and work with IP counsel. Otherwise, you could find your self facing a disastrous copyright infringement litigation.