It should fit. Here's a link to the 71 cabinet and which machines fit into it.
http://www.ismacs.net/singer_sewing_...ny/71_cab.html
It sounds like someone has messed with it though. There should be prior hinges that the 301 cradle hinges fit right into and screw in. If I were to guess it's almost like someone already took a buzz saw to it already, to enlarge the opening:<