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Hello. My name is Tan.
This is more likely a shift cable issue. When the shift cable going to the drive gets stiff it will cause unpredictable shift issues. Starting with stalling of the engine. When the cable starts to go bad it causes the shift interupt switch to stay engaged to long causing engine stall. It also cause slow engaging of the gears.
So we need to disconnect the shift cable going to the drive and shift the drive by hand the cablke should slide smoothly with little resistance.
The neutral safety switch only come into play during starting of the engine. The inly this it does it not allow starting the engine in gear. If engine is in gear it will not start. Once engine is running it does nothing.
Post back with findings and questions.
Which shift cable? Was it adjusted. The only thing that will cause when shifting is cable or adjustment. The throttle cable has nothing to do with this issue.