For starters, I do believe screwing the adjuster "outwards" tightens the steering box, not turning it "in". This 'should' be adjusted with the linkage disconnected, and feel of the lack of slop, etc, but many on the forum tighten in small increments (1/8th turn at a time), until they feel a slight binding at the extremes (full left, or full right turn). Too tight, and the steering wheel will 'want' to 'stay' turned all the way over.

Standard practice: have a friend wiggle the steering wheel back and forth, and watch your linkage - where's the slop? In the box, or drag-link, or tie rods?

Oh, and don't forget to check the upper and lower ball joints.
Jack each wheel just off the ground, and with hands top and bottom on the tire, see if you get play. See if you perceive a 'clunk'. Don't go at it like your tearing something apart - it only take enough muscle to lift and move the wheel and spindle unit around - finesse. You'll feel the 'clunk', sometimes almost subconsciously. If yes, it's bearings, or ball joints.

Grab the tire front and back, and wiggle. If it's the same amount of play/clunk, suspect bearings. If there's no clunk perceived while wiggled this way, but was hands top and bottom, suspect an upper or lower ball joint.

I'll also add: if the front tires have a fair amount of wear, a good front end tech can tell a lot by reading the wear pattern (but experienced techs can be hard to find). Not sure how long you've had the car, but most used cars need tires. I've learned to have the front end work done before getting new tires, not only from the obvious standpoint, but because a good tech can read the old tires - they tell a story