996 Turbo shifter failed much like your's I suspect. The ball socket failed and the shifter became detached from the linkage to the transmission.
The tech's recommendation was to replace the 996 Turbo factory shifter with the factory 997 shifter which was a bolt in replacement. The tech claimed this was a much better shifter than the shifter the car came with.
Afterwards there was no feeling of the shifter being half a gate off or off in any way. The shifter had a lot less slop/play in it and shifting was noticably improved. The tech's recommendation was spot on.
Based on my admittedly limited experience I suspect the dealer is just well, to put it bluntly, blowing you off. He is essentially giving you the explanation "they (almost) all do that"...
Unless someone can and does chime in with something that backs up the dealer's claim I would consider this action. Return to the dealer and state to the service manager that because the shifter is not right -- for whatever reason -- you are worried that the shifter with its half a gate off is going to fail and leave you stranded again. And to possibly fail in traffic and subject you to some danger. Thus you have lost all enjoyment from the use of the car.
If what the dealer says is true then some new (and used) cars should manifest this feeling of half a gate off as the same variability that resulted in your shifter being half a gate off should apply to new cars too. Insist on trying a few cars. I believe you will find no such feel that all the shifters will be ok.
If there is no adjustment to bring an outlier shifter mechanism into proper/acceptable position then the shifter should be replaced with another new one and this repeated until the shifting feel meets with your approval and you can feel safe again in driving the car.
You must show up at the dealer prepared to leave the car. If the dealer can get you to leave again with the car he's being shown you are willing to accept -- at some level -- the car is it is.
If you get any pushback from the service manager ask to speak with the general manager.