The question is what actually moves when the shift lever in the cab is moved?
1. The shift cable would be my first suspect, but you stated when the cable is disconnected from the shift lever on the side of the transmission, the shift lever in the cab with cable attached moves freely. In that case, there is no load on the cable ... would the cable start to show binding if it were to actually need to apply force to the lever on the transmission? At 300K miles, I would just replace the cable as a first step.
2. The transmission gear position switch on the RH side of the transmission. This is potentially exposed to sand, road salt, etc. and could possibly corrode internally and start to bind. Remove the switch and see if the shift stiffness disappears.
3. The internal shifter detent mechanism, a spring-loaded lever with a roller on the end that engages a notched detent sector. This mechanism is constantly bathed in ATF so should be well lubricated. It looks like the ends of the shaft pass through oil seals in the transmission housing, so if the ends of this shaft get corroded, they might bind in the housing. Dropping the transmission pan will allow you to inspect this mechanism.
Here's the internal detent mechanism, with the detent notches on the lower part of the valve lever sub-assembly
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Shifter detent mechanism seen from inside the transmission.
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