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I know it's going backwards, but the fact that nearly every Logitech mouse comes with such a converter means it's possible, right?

Nope, 'cause every logitech mouse is designed to work with their adapter. The way I understand it is that the mouse has both built in, and the adapter just triggers the mouse to "speak" ps2. What you want is something that translates the USB connection to a ps2 connection, which looks like is going to involved some active electronics.

Matthew