No play actually.
On the rack free play I had tried that route 1st with no help. The adjuster is simply pushes the back side of the rack into the steering pinion gear. The Spring under the cap does the work and getting it too tight can cause a bind. Also that bind really can't be felt with the wheels installed as the caster pulls the wheels left or right while jacked. A binding steering spooks me.
The BDR uses a flipped RHD MR2 rack.
https://toyota.epc-data.com/imgjp/B3/MCA933E.png
You probably should just replace the the steering shaft and joints with beefed up parts.
Shopping list is here. You most likely will not need the center Heim bearing I added to mine.
Steering shafts upgrade
Further details are in this thread.
Can't take any credit but you should consider Speedbrakes steering upgrade.