Hello allfordmustangs,
We require your assistance once more
.
It would seem our straight-six 1966 Mustang Coupe was at the end of a productive cycle when we bought it at the end of 2008. Since then, we've had to replace the shocks, the rear end (and associated mounting hardware), the entire brake system (thank God for kits), and various other bits and pieces. Needless to say, Johns Mustang in Houston has profited.
New problem. My little brother (it's his car) was driving it home late Saturday night when the accelerator refused to return to the idle position. The way he tells it, he was forced to stop the car, pop the hood, and push it back down in a stop-and-go journey home. Nevermind he could have bent over and pulled the peddle up, or far more preferable, called me for a tow. I'm just relaying what I was told at 3 am when he pulled in. All kinds of alarm bells were ringing, I can tell you.
I checked it the next morning and quickly isolated the cause to the accelerator return spring, and replaced it from an O'Reilly's return-spring kit late this past evening. The old one was probably original, and I genuinely expected it to crumble when I pulled it out, it was so brittle.
Now you know the lead-up to the present problem, and perhaps already have suspicions. My little brother had some difficulty with it immediately, so I had to test drive it. After putting a couple miles on it, checking shift positions, starting and stopping, etc, the symptoms are thus:
When accelerating slowly everything is okay, all the way up to high gear as well as the higher RPM's (no gauge; by ear), so I decided the engine wasn't the issue. However, accelerating at an average or greater amount from a dead stop causes the vehicle to stall/buck/shudder and the engine *nearly* dies. When accelerating "hard" while already going a high speed (already in 2nd gear, for instance, and on the way to 3rd), the engine seems to rev a little higher without transferring any additional power to the wheels. I had thought it was a shifting problem with the first-to-second gear until that happened, thinking my brother had shifted from neutral to drive at a high RPM or something, but with this new high speed behavior and the absence of any outright grinding noises my theory evolved (see below).
I didn't dare "force" it to continue whenever it happened, and instead idled and rolled to a gentle stop while the engine recovered. This dead stop acceleration behavior remains consistent across all 3 forward shift positions (dot, circle, & L). Since it was night, I did not test fast acceleration in reverse.
I would consider myself mechanically inclined, but I have not checked how an automatic transmission works. I have the shop manual for the car, but it's too late in the day and the automatic transmission section is substantial all by itself. My standing (ignorant) theory is that, since the general shuddering/halting/odd behavior does not appear to be specific to any gear, the problem has to do with something between them and the engine.
Any help or advice would be appreciated. Any solution has gotta be something we can do ourselves, no shops can be involved. The local mechanics are uniformly corrupt where they aren't incompetent. (Maintenance on half a dozen family vehicles, avoiding repeats at bad shops, quickly brought us through the entire selection and left us bitter.)
1966 Mustang 200 6 Cyl; Automatic Transmission Shudders @ Acceleration 
