Note the steering box issue:
I have a VW Beetle and some time ago when I replaced the steering box, I too adjusted the play by turning the adjustment bolt...you can tell by steering which way to adjust (yes, counterclockwise).
All that does however is give you a tighter "feel" since the adjustment serves to tighten the load on the steering shaft. You adjust the feel on a new or rebuilt unit to suit your taste...but it doesn't really solve the "play" issue.
The culprit is worn components, period. Adjusting the steering box bolt is a Band-Aid fix, comparable to raising the idle speed to solve a rough idle problem.
So having the steering components replaced was a sound decision. And yes, vacuum leaks plague many vehicles with rough running issues...it's a shame most owners start throwing parts at the problem first!