Need advice with steering problems

My 1937 Dodge coupe has always had "sloppy" steering. The tie rod and drag link ends looked worn so I replaced those and it got a little better, but there is still about a quarter turn worth of play in the steering wheel. The play isn't really bad or even noticable at slow (parking lot) speeds but once you get on the road (25mph+) things get scary.

I'm guessing that it has to to with the steerign box. Would this play indicate a worn worm gear or bad bushings? It seems to me that bushings would wear out before the gear teeth would.

I've got the adjustment screw tightened (as shown in the shop manual). Is there a way to diagnose the problem so I can order the correct parts before I tear into it?

Tarren Shaw

Stillwater, OK