Really sorry for you Martin, after reading this thread. You were so excited and pleased when you bought the car. The fact that you got a full refund from the dealer is the only bonus, as you are not too much out of pocket.
Lexus cars are complicated and if you are (VERY) unlucky then the costs spiral to the extent it can write-off the car. Thank goodness this happened so soon, as had the warranty expired you would be stuffed!
My gut feeling would be to get a LS430, but has you had a bad experience with one, I understand your reluctance.
There are basically two options, as I see it, if you want another GS450H. You will need to buy one with a Lexus warranty - that way you will have peace of mind. But that will cost a lot more. Or go again for the "cheap" end of the market but be prepared to risk the money you have paid. It is a balancing act, but at the luxury end of the market you are much better off buying an old Lexus than a Merc, IMHO.
My friends Peugeot has just cost £1,400 AND it is still not working - goes back today!
If you have the time, knowledge (from this wonderful forum!) and patience, they can be run at a reasonable cost. Your problem is that it is your daily car and having it off the road is real pain.
I would be interested to hear your thoughts after some reflection.
Going as cheap as possible, expecting the worst and hoping for the best is one option.
The other is spending a lot more for one with a warranty.
Good luck with your search Martin.