The only hope might be the HOLD recording mode for pickup machines. I didn’t get a chance to test it this morning, but since every time you press (and HOLD) the Rec AB button it overdubs, that mode just might preserve the buffer contents after pressing STOP.
If that doesn’t work (i.e. the first time you press Rec AB the buffer is cleared) then there’s definitely no way to do it with just 1 pickup machine track.