Transmission Shifting issues

Recently my transmission has lost fourth gear and after reading some I have decided that it is more than likely the 4th gear shaft, or whatever the correct term for it may be, since the car has 160k miles on it. I have decided to go ahead and pull out the transmission but I am trying to decide whether to replace just the shaft or go through it. I think that 3rd gear may be having a minor difficulty engaging in this car but I don't know what is correct for these things. Could someone please post a video of their tachometer when driving their gtp in non-performance shift mode with enough throttle to make the car shift at around 2500rpm. I need to see what is correct to decide whether or not to tear into the transmission itself.

For specifics I know the 1-2 shift it fine, but when it shifts into third the rpm's don't change from 2500rpm for a couple of seconds, then it is as though the torque converter locks up and the rpms fall to about 1500.

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