The white cams that look like top hats (but really are not the same) are Flexi cams. Later machines.
There were some really funky machines that Singer made with different cams, much later... up into the 70's and even 80's... but so far, haven't been able to find an exact match. Been tryin! There was a needleplate on ebay for sale (with one of the needleplate numbers) thought maybe that might give a clue. But the seller had no idea what machine it came from. And the singer site doesn't allow you to search simply by part number. You have to know the machine first. Judging by the higher part number, those odd cams are from a later machine than the 600's or 700 series.