1977 bird c6 transmission problems

I just bought a 1977 Thunderbird with a 351w about 3 days ago. It was daily driven with no problems for 2 years then sat for about a year before I got ahold of it. It runs and drives, albeit a little rough, but good enough to get around town. It has a pretty big cam in it and i believe it has H.O. heads from a 1985 351w. The main problem that I am having is that, for example, when I slow down and stop at a stop sign, then let off the brake and proceed to accelerate, the engine just revs and the car goes nowhere for about 2-5 seconds then the transmission kicks into gear really hard and the car accelerates/everything is back to normal. It doesn't slip or anything at any other time, this is the only transmission issue I'm having.

This is the first carbureated vehicle I have owned/driven; everything else I've driven or worked on was fuel injected/electronic plus I'm not very familiar with the functionality of a transmission itself. I've asked a few technicians at work what their take on it is and they suggested that I check the vacuum line going to the modulator valve for leaks and/or replace the modulator valve. I believe the modulator valve was been replaced by the previous owner when he drove it. I plan to perform a tune-up and try to find/fix any vacuum leaks this weekend in the hopes that maybe this will alleviate the issue.

The reason I am posting here is to see if anyone else has encountered this problem and to seek advice on how I should go about fixing this.

Any advice or knowledge is greatly appreciated!! I have lots and lots to learn yet.
The vacuum line should go from the carburetor or around the carburetor and down to the modulator on the trans. Have it running and pull the line off the modulator and make sure you have good vacuum there. Make sure you don't have or you can't hear any vacuum leaks anywhere. It will make a sucking or hissing sound. Carburetor should have a few vacuum lines on it big and small. Pull the dipstick and make sure the fluid isn't dirty brownish color or smell burnt. If it is or does smell burnt change the fluid and screen filter on the bottom of the trans inside the pan. Sometimes the torque converter will have a drain plug near the bottom where you can drain it also. Should be an access plate on the bottom where the trans bolts to the engine to get to the drain plug if there's one.
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