'66 America - rebuild motor?

Hey Guys - I have a '66 American (199 cu) that I'm having some trouble with and could use some advice. A month or so ago I asked about a flat spot and received some help, but none of it worked. The engine starts right up and idles fine, but when you put it in drive it stalls once you step on the gas. You can power your way through it, but at times I can press the gas pedal to the floor and there's no power and at other times it runs fine. I've tried advancing the timing, changed the points, rebuilt the carb, and the problem still exists. Any help would be much appreciated. Thanks!

I too believe the camshafts on these engines are on the verge of running retarded. Just changing the timing set and a warn out rocker assy perked mine up a lot. Although I know it is not yet as good as it could be, it doesn't hesitate hardly at all anymore and  fuel economy is way up.
When I get to my next one I will add the Crower cam I picked up in California.

Frank - that's ok watching a rocker (I suspect you meant "note a rocker arm" and not "not a rocker arm" but I personally find pulling the distributor cap and watching the rotor is a bit easier - it will show movement almost instantly where the rockers you really have to stare and pay attention.

OK, no offense, but did you rebuild the carb, or just clean it up and put the new gaskets in it?
The accelerator pump may be "shooting a stream", but it's a calibrated stream, and may not be enough. You can't just say "yes it's shooting gas in, thus it's fine". There are adjustments in a majority of the carbs for the accel pump - when it starts, when it stops, the duration and amount of fuel. Too little and you have hesitation, too much and it's a waste and runs rich unnecessariliy.
the air bleeds, tubes, passages, off-idle circuit, all need to be very carefully checked for dirt and gum/varnish. Standard carb cleaner in a car is great for removing black sooty deposits but frankly won't cut the tough stuff inside the passages. That takes a real chemical like the buckets of cleaner - the soaks.

How about double-checking your float level, too. Too low and it will run lean and HESITATE.
Next, check the fuel supply - remove the line to the carb, run a long hose to a gallon jug or jar and start the engine - watch for flow. If you have a gauge, check fuel pump pressure. Since it "at other times it runs fine" that sounds less like a mechanical or physical issue such as timing set, more like a transient issue - lean, etc.
If it was physical, it would always be there, hot or cold, today or 3rd Tuesday of the 5th month after a blue moon, any day.

The vacuum advance on these should kick in, or come into play as you get off-idle - to help cover that hesitation. No advance when it idles unless the fuel system is messed up and the throttles have been opened (idle set up) to compensate - THAT will cause hesitation, too. If the thing is too lean at idle, or has carb issues, then often folks will simply jack up the idle screw to get the idle speed they need or want, but then they are into the off-idle circuit, the vacuum advance is already kicking in, and further, the accelerator pump system won't function correctly as the throttle is already partially open! People don't realize how much they mess up when they cover an idle issue by simply screwing in the idle speed screw to get it up to speed. It's a system - and if the idle can't be properly adjusted and the throttle plates kept nearly closed at idle, you mess up a whole lot of stuff. You think you've simply compensated for an idle circuit problem by opening the throttle plates, but what has happened is that 2 other systems designed to prevent hesitation have just been compromised or disabled in the process.

You should be able to slowly accelerate the engine and see it advance (did these distributors have the open vac advance link on the outside visible, or was it contained like some of the very late units? If visible, one can watch it as one opens the throttle - and watch it advance)

A cam running retarded or advanced only shifts the power and torque bands up or down..... won't take power away necessarily. Stock cams are a balance of drivability, economy, power and power/torque high or low speeds.
After-market cams allow you to decide which you wish to give up in order to gain one of the other.
Unless there's excessive wear on this cam, I'd not even count that in the equation at this time.... there's something else afoot here.

My first advice, unless you are trained in carburetors or had it done professionally - pull the carb and double-check your work. My guess is there's a fair chance there was something not done, not set correctly, or still dirty. Set everything by the book - don't skip a single step in the instructions. Make sure the float level is EXACTLY at spec, same for any adjustments for accelerator pump and so on.
Miss nothing.  Attention to detail is critical here.  A torch tip cleaning tool CAREFULLY USED can be your friend. (doesn't hurt that I have all the original AMC/Rambler/Kent-Moore carburetor tools of that era, though)

It looks like I have a lot to work on here! The carb was rebuilt by a professional, but I can have him go back over it. Someone recommended advancing the timing a bit and when I did that the car ran great with twice the power, but only for one spin around the block. After that it sat for an hour and went right back to stalling.

Also, it shifts hard into reverse - is that common?

Thanks!

Shifting hard into reverse is likely caused by the higher idle from advancing the timing. When the engine is worked out that should go away.

Check the vacuum advance. Disconnect the vac line and plug it (so no vacuum leak). Get another piece of clean line about 2' long. Connect that to the vac cannister. Crank the engine then suck on the line on the cannister. Engine speed should change. If not, the vac advance isn't working. You can also pull the cap and look at the plate in the dizzy to see if it moves when you suck on the line. Of course if you have a hand held vac pump use that...