Lining up the marks is essential. Adjustment is made when the wheels are exactly in the straight ahead position. On an unworn box there will always be a bit of play at the steering wheel. 1" to 1 1/2" either side of centre is good but although the manual shows adjusting on the bench with a spring weight gauge doing it by feel is fine. It mustn't be adjusted too tight. With the front wheels off the ground, jack stands under the lower A arms there should be no tight spot when you move the steering wheel across the centre position.
New steering worms aren't available, they are part of the steering shaft. Box can be rebushed and reshimmed. This will not revive a box with a worn worm. If the lower bush is worn it will allow the shaft to move and that will quickly wear a new seal and it will start to leak again but just a new seal may cure the leak for many more miles. Easy to fit with the Pitman arm off.
A basic idea as to how much wear the worm has is by looking at the number of threads showing above the adjuster lock nut. 2 is good, 1 is pretty worn and less, very worn. Adjustment is still possible at the expense of more free play in the steering but with this design of box this play is always there to some degree and you get used to it. If you move the arm on the spline you will get a tight spot when you're driving and when cornering it will feel pretty nasty when a bend matches this spot.
Grease is not advised as it just clumps and dries out. If going with that idea there are some liquid steering box greases which do flow and are about 160 weight. Getting out the grease you have put in will be a problem.
What to do? Check the old box for worm wear by adjusting on the bench and reviewing the number of threads on the adjuster. Check for movement on the lower bush, If OK replace lower seal. If you're up to it dismantle the whole box. Wash and inspect everything, Check worm for wear marks and galling. Rebuild if OK. Consider rebuilding with new bushes. They need to be reamed to fit the shaft. A kit is available. Eric may comment on this and maybe able to offer that procedure.
Good luck.