Hard shift to 2nd and 3rd

Let me start off with my level of knowledge in transmissions is nil. With that I have an issue and I am trying to figure out how and what I may need to do.

I have a 1965 Barracuda automatic. I believe it is a 904 torqueflite I could be wrong. When driving the car the shift from first to second is hard. I call it clunking. You can physically hear and feel it engage. I get the same thing into third. I called a local transmission shop and he suggested a vacuum modulator. I checked into that and it appears Chrysler did not use a vacuum but a mechanical kickdown.

Some background on what I have done and seen. First I changed the trans fluid and gasket. That did not help. While I was under there I noticed a box with what I believe to be one of the shift cables towards the "back", drive shaft side, of the transmission cover that had some silicon on it. It is near where the speedo cable goes.

So can anyone suggest what I can do or should I just have it adjusted by a professional? If a professional what kinda of cost might I expect.