been reading this thread with a sense of 'this is going to end in tears',I really do hope I'm wrong.
Firstly,if a 13K car is not exactly what you want ,walk away.If it was a £1300 car then yes you would need to compromise but for 13k you will get the right car eventually.It is out there somewhere.
The other thing that struck me was that you are expecting these cars to have problems and I think you are wrong.Its not an Alfa (as an Alfa enthusiast I have owned several and love them )these cars are well built and don't really carry any inherent problems apart from the 'flat battery ' problem when they are left standing.Not sure if this affects the later models.
The 'faults' you mention did affect a few cars but it was never the norm.
You will need to personally check these 'fault' items on any car you are considering as relying on someone else who has a vested interest in selling the car would be foolish to say the least.
Which brings me onto your reliance on Lexus dealers to be honest,professional and have your interest at heart.Sad to say the exact opposite is the way it is ,main dealers ,including Lexus,are the biggest bunch of sharks you will come across.
I would suggest you bear this in mind in all your dealings with them.
I drive an old SC430 (01 vintage)with the 5 speed 'box,it is the best auto box I have ever driven and perfectly adequate for normal driving so I wouldn't get too hung up on the 6 speed 'box.
I wish you well with your search/purchase,keep us posted on how you get on.