I would start with taking yours apart to see what is actually bad, my be able to be fixed.

The Filling Station (ad top of the page) sells rebuild kits and parts. I think they used to offer rebuild services but don't see that on their web site. You might give them a call. If they no longer offer a rebuild service they can probably direct you to a competent shop that can do it.

I have one but it is used and hard to determine how worn it is. Where are you located?

Hello, My 31 was like that when I bought it. Although it appears there is only one adjustment there is a way to loosen the 3 bolts that hold the box to the frame one of which is on an eccentric cam. I was able to go from a third of a turn of play down to nearly nothing. I can not remember where I read about the procedure but I believe it was in the November 1930 Dealer service news. It may have been posted on this old forum. Hope this helps  

It is first necessary to determine if the two bushings on the pitman shaft have not worn. It is very common for at least the outer of the two to have significant wear. The is often caused by grease instead of flowable oil added to the steering box. The fact that a zerk fitting is found on the steering box. Someone has replaced the original alemite heavy oil fitting. Grease will not flow to the outer bushing. Replacing the bushings is not too difficult. Once that is done then the two adjustments can be tried. First is checking for condition and then replacing and adjusting the upper and lower ball bearings on the steering shaft. Once that is done then the box adjustment can move the pitman gear to better mesh with the worm gear on the shaft. A good dose of flowable grease should tighten the slop and give acceptable steering.

I'll have to wait until I can remove and disassemble the box to determine the condition, unless I can find a decent used one somewhere. 

I'm outside of Nashville, TN

Is there a recommended flowable grease for these steering gears ?

@a-william-toomey 

Short answer is... yes.

The grease should be as you said flowable and non channeling, and thus of the NLGI grade 00.

NLGI 00 greases can be hard to find in small quantities, so many people either use John Deere corn head grease by itself (which is NOT flowable or thin enough by itself as it is an NLGI 0) or they mix oil with it.

There IS however a better alternative.

FYI, Bill Barker has quite a website full of info about 1931 Chevys. Here's a link: https://1931chevrolet.com/

Cheers, Dean