Your machine should be a standard low shank. I just looked at my Singer 99. The flat of the presser bar appears to be lined up with the needle. I think the shafts themselves are offset a bit to help this happen.
I think Kenmore did have a proprietary system. I think it was a super high shank, not a low shank though. You should be fine with any low shank foot.
Good for you for keeping your promise to your daughter.
Rodney