I looked mine over, and there is no way the round bar one would work with yours. I've looked and looked for pictures - and I have found the controller that looks like yours working with the flat end knee lever - but I have not found any picture showing the hole well.
I have yet to encounter a Singer knee lever of a different type than these two - but it could be out there. Or there was something that fits inside the hole to narrow it down for the flat bar - I'll keep looking.
This listing does have a picture of the controller like yours. The one the round bar fits into is quite different looking.
http://www.ebay.com/itm/Vintage-Coll...item19f1e82c9f