Thanks for anyone who suffers through this post. I put in some pictures and an animation to make things more interesting.

The configuration: 318 block, chrysler 360 heads, chrysler 360 intake, holley 4360 (450 CFM) carb (just rebuilt), mechanical distributor (just installed rmfd), MSD 6A ignition box, MSD blaster 2 coil. Let me just point out that the long block and ignition setup were in the truck when it came to me. Don't blame me for them!

More details with images and animation:
When the engine is cold and I start it without the fast idle cam dropped on the carb, it will fire up w/ about 13 to 15 inHg on the vacuum @ about 500 RPM and run for a second or two during which the speed and vacuum falter and drop steadily until it stalls. Do this twice more and it will stay running and idle roughly at about 650 RPM w/ 15 inHg on vac gauge. If I put it in neutral and let the clutch out, it will drop to 500, the vacuum decreases to < 14 and often it will stall. For giggles, I looked at the timing during this stage and it was > 5 ATDC (that's right, after). If I try to accelerate gradually, at just under 1k RPM, it will miss and backfire through the carb and often stall. (Now my freshly cleaned and rebuilt carb is black inside, my air filter is dirty and the clear vacuum hose I put on the vacuum gauge is black inside.) Fast forward 5 minutes of idling in the driveway and the idle speed will be closer to 800 RPM and the timing closer to TDC with vacuum ~ 15 inHg. The engine is warm but I haven't driven it and the RPMs haven't exceeded the idle. Now, if I put it in gear (or leave it in neutral) and try to accelerate gently, at precisely the same RPM (~1k) it will backfire and almost certainly stall. If I got it rolling, I can pop the clutch to get it started again. Often, I can double pump the accelerator to get it past the 1k kill zone and into 1500 to 2000 RPMs, then burn the clutch to get it moving. Not my favorite way to start out the day. Now, fast forward to the first stop light. I've had it up to 2000 or 2500 RPM on the way and at the stop light, the idle has risen to just over 1k RPMs. If I check the timing now (yes, I've done it at a stop light in the predawn hours), it will be ~ 8 BTDC and the vacuum can be 18 inHg to 20 inHg. As the idle is above the dead-zone in RPMs, it will accelerate fine with no backfires. If I leave the clutch engaged as I'm pulling up to a stop light and bring the total RPMs down below 1k RPMs before I put the engine in neutral, it will idle at a lower speed, i.e. 800 RPM (15 to 17 inHg) and I'll have to suffer through the 1k stall zone. Deceleration does not trigger the stall as It drops below 1k on accel. Same thing happens if I change from 1st to 2nd early and the RPMs in second fall below 1k RPMS. I've found and fixed a couple of vacuum leaks, e.g. the carb choke pulloff can (converted choke to manual), the distributor vacuum advance can (put on a new distributor and can, thanks to robertob for pointing me at the can). After it is warm, regardless of where the idle is, at idle the vacuum is steady. I rebuilt the carb. New plugs, filter. Strong spark. All of this has improved power, smoothness, etc. above 1k. The dead band remains unaffected.
OK, so the question, so what is the origin of the 1k accel dead zone? I'm also curious why my idle is dependent on the previous state, e.g. engine speed fast (i.e. > 1k) or slow (i.e. < 800 RPM).
So, one more thing, possibly a red herring: When the engine is cold and I'm in that low RPM idle state I hear a loud 'clack' from the driver side of the engine, at (I think) engine speed. As I mentioned, for giggles one morning, while it was still cold and making this noise, I put on the timing light and it was > 5 ATDC, maybe as much as 10? I quick-like loosened the distributor and advanced the timing 10 to 15 degrees and the noise all but went away. I put the timing back to where I had it from when I set it while it was warm. If the engine is warm but in that lower idle speed state, this sound will be heard, though more quietly.