I think the stock limiter is either 174 or 184 MPH on the speedo (which reads fast at those speeds anyway, so actual speed will be lower), so that's not an issue. It's definitely over 170 though.
Limp mode is definitely a problem, get it to the dealer. 8600 RPM shouldn't be possible either but as you may have noticed the red zone seems to start around 8250, not 8400, so there might be an inaccuracy there too. Still, while these engines are built tough, I wouldn't sit on the limiter for extended periods. There's a reason that earlier part is yellow; consider that a reserve area.
You may indeed have a tune; if you contact a local tuner they may be willing to check your car for free and confirm?
'16 Cayman GT4 (delivery pics
Gone but not forgotten:
'11.75 M3 E92 Le Mans | Black Nov w/ Alum | 6MT (owned 5/2011 - 11/2015)