I showed a picture to a friend of mine that collects badged machines. She has quite a few and is pretty knowledgable. But she always double checks.
Here is what she said
This looks a lot like my Texas Advocate. I couldn't find a machine labelled "Red Cross" on Needlebar.org, but I'd bet this was also made by National --- OR --- Davis given that the belt is on the outside of the handwheel. It is NOT a Singer machine. I've never seen any Singer machine with the leaf tension or the belt on the outside of the handwheel.