Does applying for a DTV invalidate an existing Non-O visa?

To the best of my knowledge, the DTV would indeed invalidate the non-O if it's approved before entering. If after, you'd enter a bit of a special situation where you are staying, like we say, "on a visa", but technically that's not the same as "having a visa". A visa is a document valid for entering, once you're in the visa is used. So if my first answer was wrong you could even make it work, applying shortly before the flight. Then for yourself, indeed just leaving without re-entry does the trick (although thinking again if you have one it would just be invalidated but obviously you're not getting one if you want to get the DTV).

You would have to LEAVE Thailand without a re-entry permit...

Then if you get a DVT visa elsewhere..

Enter Thailand with it.

Unless I'm greatly mistaken you can't have two valid visas which haven't been used. (other than elite and another visa type but elite is a special situation)