It is not uncommon for the "idler arms" on your Astro van to wear causing loose steering. There are two idler arms on your van and both can wear. I would suggest you have the front steering linkages and suspension checked buy a qualifed technician. The front end alignment should be checked and set to specs if the idler arms are replaced.
this answer is useless
it is easy to point out the weak parts on a vehicle
a little harder to answer the right question
idler arms have no part in front end alignment adjustment-disregard
yes, you can adjust your gear box, it is just not very likely that this will fix your problem.
when the gear box wears out, as in a vehicle this old, changing the position of the gears will tighten it up but also could cause it to bind in the future, you are probably in need of a replacement gear box, which is fairly easy to do and will cost around $125 for a reman box.
if you haven't checked you idler arms do that FIRST, then check all the linkage as this is good advice
i assume since you are looking at the gear box that you see the linkage is good and the play is obviously in the box
this is one of those things astro vans do at around 250-300 thousand miles