Yeah, I saw that space underneath the steering wheel, and thought you probably had a pretty sloppy column....It's just worn, and can be rebuilt. It is a fairly common problem, especially with the tilt columns...I'd start by Googling GM steering column rebuild , and check out the hot rodding sites like the HAMB to see if anyone has done a how to on your particular column . If you wanted a more vintage looking steering wheel, again, look for an aftermarket wheel to fit a 70's GM car... Are there any identifying makers marks on the column or wheel anywhere?
Take a few good pictures of the rest of the steering for us...make sure the box is mounted securely to the chassis, no cracks in the frame rail where it mounts.
I'm not a Saginaw steering expert, all mine are stock. However there are members here who have done the conversion.