I think the previous advice about having someone turn the steering wheel and checking for play outside the steering box is pretty sound. There are a lot of other components between the steering box and the wheels that can all get plenty of wear- tie ends, drag link adjustment, king pins, etc. It might not
necessarily be your box.
But it could be.
Before I pulled my box, I took off the side cover. It was packed with what looked to be ordinary grease. Since the box is sealed up pretty good, gets a minimal amount if wear (comparatively speaking) and doesn't heat up much, there wasn't much gunk buildup in it. As far as I can see, there wasn't a drain, only a plug in the top for adding lubricant. There was a lot of gunk built up on the outside of the box, no gunk inside.
BUT what I did find when I started digging the grease out with my fingers was a bunch of loose ball bearings and metal shavings. The bottom cup had broken sometime and the nincompoops who owned it at the time just kept on truckin'! There were actually grooves cut in the cast iron when, apparently, some of the ball bearings found their way between the sector and the housing. Probably got stuck and the idiots kept yankin' and crankin' until it freed up again!
So needless to say I rebuilt my box. It took a long time to find some "good enough" parts and if I were faced with the same situation I would probably send it somewhere and have it done for that reason alone.
If you do open it up for an inspection and cleaning, I would think just using parts cleaner and a brush would do the trick, but it would be awkward and messy to do with the box still bolted onto the frame. Blowing the cleaning fluid out with an air compressor is probably a good idea to keep from diluting your lubricant. I've read many posts suggesting Lucas hub oil and that's what I replaced the grease with in my box- supposed to cut down on the leaking. Once the side cover is off, be careful you don't disengage the cam rollers from the worm gear. The side cover is what keeps them together. If you do, it might not be the end of the world, just make sure that neither the wheels or the steering wheel moves while they are apart or you face an entire readjustment/reset process which, while not rocket science, is a bit of a PITA.
If you get her cleaned out and all's good, there is a method to tightening up the adjustment screw outlined in the shop manual (which BTW is an excellent purchase- get it from Binder Books). There is also a neat little device called the Tightsteer available. Basically a spring loaded adjustment screw that keeps the steering adjusted automatically:
http://www.siminoffjeeparts.com/TightSteer_FAQ.htmlSorry about the long post, but I've been down this road myself. Hope I answered some of your questions. If I'm wrong about anything, someone with better knowledge please feel free to correct me. I'm still learning and might have made a mistake or two in the way I did things.