[Marshall V. Daut]

If there's grease in the steering box, you can bet the sector gear teeth are worn and will show shiny signs of wear divots on their faces. This will create loose steering play at the steering wheel because the sector teeth no longer make full contact against the worm gear. Chassis grease is death to Model A steering boxes! You're at the stage of disassembly where it makes sense to install a new seven-tooth sector gear, which will reduce slop in the steering.
If you can't afford Penrite Steering Lube (kind of pricey for a one-time filling), mix equal parts of STP oil treatment and 600w. I hear pros and cons about Cornhead grease. No personal experience with it. The STP/600w mix will do the trick to lube the gears and reduce leaking, although not as well as Penrite.
Marshall