when it sat up the valve stem seals hardened because they wasnt coated with oil for awile. this allows oil to get past the valves from the top of the heads and get in the combustion chamber. when you first take off it stalls cause the oil in the gas mixture reduces the gas's flash point, and it hesetates, when you speed up your valves are moving faster and its harder for the oil to pass past the valves, this is why it quits smoking at faster speeds. also this is making the oxygen sensor in the catalytic converter read an undesirable reading, causing it to tell the map sensor to close the flap in your air intake and choking the air flowing into motor, onee thing affects the whole system.
now how you could cheaply try to remedy this, transmition fluid rejuvinates rubber, makes it swell and makes it soft and pliable agian, thus the valve seals will seal good agian.
do this..... take the intake hose off the throttle bady or the carb whichever you have. now have someone get in the car, start it up, and give it a little bit of gas while you yake about a cup of automatic tranny fluid and slowly pour it into the carb/throttle body. dont pour it in so fast it kills the car. this will soften the valve stem seals back up, and also cleans the varnish and gunk out of the engine.
now dont be surprised when it start smoking horrendously, dont worry it aint hurting anything, and will subside after it burns all the tranny fluid out.