Welcome! Glad you made it on and congrats on the purchase. Cool to know you're the only one in the country with one, that's awesome.
Sounds like a great plan, there's definitely some aftermarket touches on this, but nothing wrong with that and it looks great.
On the steering, the kind of play you're talking about in the wheel will not be helped with a steering stabilizer (and don't bother with the dual setup, one is all you need) except maybe to cover up the problem. You'll need to find the source of that much play. It's not unusual for something/everything between the steering wheel and the tires to need to be replaced (I don't quite mean that literally) to get the steering to be properly tight. There's lots of good threads on here about things to check to fix loose steering. A stabilizer is only there to dampen hard bumps from potholes, rocks and what not, otherwise you should be able to run without one and not have any issues on smooth roads.
Welcome again and congrats on the find after such a long wait!
That Jeep looks like it is in pretty nice shape! I can see that the paint looks good, even with mud over it. Send those seats over to me on the next boat to America -they're a perfect color for those hot top-down days. They'd go great in my FSJ!