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sounds like you might be experiencing a low pressure condition maybe the pump in the trans is failing as you can compensate by adjusting the cable to increase pressure
to fix it yes if thats the prob for sure... but a shop can check the pressures with guages and if it needs a pump might also need a rebuild as loss of pressure more than likely means loss of lubrication resulting in wear on the internals... a jdm trans might be a option...
I just went through this same type of problem - tranny guy called it "morning sickness" where the pump can't get enough pressure to get the fluid circulating. I had to have mine rebuilt with new pump, internals and a new flywheel....