Thanks for the suggestion, but I just disabled all music, synced, then re-ababled music, and synced again, and no luck.
Within the iTunes Library is where I checked and set not to remember. Both by getting info on individual songs, and by selecting a whole playlist.
When viewing the iPad in iTunes device list, the remember setting is grayed out.
Just realized something else. The remembered point is fixed. Playing or setting the song to a different playback point does not change the point at which the song will begin playing next time.
Very odd, considering there is no problem when played within iTunes!