If a previous owner had put grease in the steering box, you can bet that the two-tooth sector teeth are history. They will have deep wear grooves in them, sometimes on both sides of each tooth, but usually in the centers. No amount of adjusting will get the play out of the steering action if there is wear on these teeth. The wear to the worm gear is harder to judge, but it's there, too. Worn sector teeth + worn worm gear + worn sector bushings = unadjustable slop.
These gears were not designed to operate with grease as lubricant. The problem with grease is that it does not cling, so after a few turns, the grease is squeezed out from between the sector teeth and worm. The lack of lubrication leads to metal against metal contact, prematurely creating wear. A lube such as 600w or equivalent (Penrite?) is needed because it will cling to the gears and constantly lubricate the gears and bearings.
If you have established for sure that none of the other steering parts are loose or worn, you are looking at pulling the steering column out and replacing at least the worm and sector, as well as the sector bushings, which because grease could not enter the sector housing to lube the shaft, will also be worn undersized. If a zerk fitting is present in the sector housing, it was intended for introduction of lube, not grease. Such a zerk fitting is often retro-added to a two-tooth, but standard in the seven-tooth. Originally this fitting would be used at Ford dealerships for high pressure introduction of fluid lube, NOT chassis grease, as so many misinformed restorers mistakenly do.
Marshall