Starting to sound like a bum transmission. if it is lotsa ruck as they stopped making rebuild kits many moons ago.
The two biggest problems with the first Falcons was the weak transmissions and lack of brakes. Other then that the early Falcons, when new, would have no problems with today's traffic and would give 24-30 MPG. Won't pass the smog tests but...
Back in 1962 our family pulled a 12' Shasta trailer from Central Ohio to LA and back with only automatic trans overheating problems (we should have had an inline cooler). That was back before Route 66 was replaced by interstate highway. | 
