360 Questions.. pardon my ignorance.

This happened to me once and it ended up being a reverse polarity at the pick-up coil. This sent the ECU into a dither and it couldn't figure out exactly when to fire. Funny thing is it would idle just fine. The strobe only went whacky when the rpm began to rise.
Quick question;
Why are you trying to idle a pure-stock 360 at 1000 rpm, and 14* Idle-Timing. If you're having issues at 600rpm, figure that out first.
**********************************
Here's a tip:
24 years ago I had a 292/292/108 cam in my Hi-compression 367, and that beast was able to idle down to 550 in gear (manual trans) and pulling itself with just 5* advance. The point is; that what you think is making the engine happy, may not be.
A miniscule stumble, such as you describe, is usually called a Tip-In sag, or a momentary hesitation. This is almost universally caused by the the Transfer Slot circuit having been put into sleep mode, by the throttle being too far closed; and the closed throttle is almost universally adjusted so, because the timing is overly advanced.
So Try;
backing the timing up to maybe 6*(VA disconnected), resetting the Idle speed to 600 in gear, and twiddle the mixture screws for best quality idle. Then connect the VA to the sparkport. This assumes the fuel-level is set correctly, and that ALL the air that the engine is getting, besides the PCV, is coming in past the throttle blades. If your intake is sucking air from somewhere else, all bets are off.
Now, once you have the engine idling nice and the tip-in sag cured, only then can you try more Idle-Timing, say 2 or 3 degrees atta time, until the tip-in sag returns, then back it up .
If you try to set the Idle timing
by highest vacuum, your timing will go into the twenties and/or thirties, and your idle rpm will rise way to high, resulting in the trans banging into gear, and a mighty Tip-in bog. Forget this method.
AFTER
you have got rid of the tip-in sag, and have sneaked up the timing as described above,
THEN you can install the vacuum gauge and twiddle the MIXTURE screws for highest vacuum at that idle speed and at that timing COMBO; But DO NOT TOUCH THE SPEED SCREW.
Be advised that,
with the factory carb, distributor, and the factory stall convertor, it is as good as impossible to satisfy the engines appetite for Idle-Timing and and and, still be able to put it into gear without a mighty bang from the transmission and most likely it will stall as soon as you touch the throttle, if it hasn't already.
Whereas, retarding the Idle-timing only makes it idle slower and slower until idle vacuum is too low to support proper fuel delivery.
@Oldmanmopar provided an excellent image of the transfer slot exposure, that if you set your throttle like that, it will solve your stumble, after which, DO NOT READJUST THE SPEEDSCREW. To adjust your Idle speed, you will now change your Idle-Timing. Do not care about the actual timing number, your idling engine does not care. Job #1 is to get rid of the Tip-in hesitation.
IN ALL CASES,
after the idle-timing has been chosen, the POWER TIMING has to be revisited and modified accordingly.
Can you run 13/14 degrees at idle?
IDK;
maybe yes /maybe no
For sure NO!, if the Transfer Slot gets closed off while reducing the Idle-speed back to a sane number like 600/650 in gear.
*************************************
BTW,
when you get done balancing the T-Slot fuel, your Mixture screws should be close to in the center of their range, which on a Carter 2bbl is about 2.5 turns out.
You can use that information like this;
Set the mixture screws to 2.5 out and leave them there. Reset your Idle-timing to ~6*. reset your idle-rpm to 600/650 in gear.
Now, twiddle the screws for best quality idle. Then count the turns out to achieve best idle.
What to do;
1) If your mixture screws are out to 3.0 turns or more, then you need MORE fuel from the T-slot exposure, so increase the speed screw, then put the mixture screws back to 2.5. If the Idle-speed goes too high, then retard the timing, then verify best quality idle.
2) If your mixture screws are 2.0 or less, then you need LESS T-Slot exposure. so reduce the Idle speed, and crank the Mixture screws back to 2.5. If the idle speed is too slow, add timing, then verify the twiddle.
3) Whatever the Idle Timing ends up at, that is the limitation of your current SYSTEM. If you want to change it, then you will have to modify it.
But let me re-iterate,
the automatic transmission equipped engine does not care about Idle-Timing beyond what it takes to get rid of the Tip-in sag, and not bang the trans going into gear.
The First time your engine cares about timing is at WOT stall.
Then again at WOT after ~3600, where detonation has to be avoided at all costs.
A manual-transmission car has different needs.
Ok so
Happy HotRodding

PS
Yes, keep the VA.
AFTER the Idle timing is bugged out,
AND the stall-timing has been established,
AND the Power-timing is fixed,
AND the dots have all been connected by rate(s) of advance;
THEN comes tuning the VA for Part Throttle Performance,
and setting of the cruize-timing, which can greatly increase your fuel-economy; "greatly" being relative.
Honestly, you're looking at a percentage increase of maybe 10 to 20 percent which will depend greatly on your current combo. If you're only getting 10 mpgs without VA, then 10% is just one mpg.
But if yur getting 20 mpgs, then 10% is 2 mpgs. and that can grow to say 15% by reducing your cruize-rpm, or even to 20% by optimizing your chassis, and/but this does not take into account driving style, nor towing.

But, if you have a Holley 2bbl on it, all bets are off. That POS carb is just way too lean. I only ever got to work on one of those, for my younger brother, in an old Van. Good Lord that thing cost me hours of modifications. I thought I would come out on the losing end of that deal. But in the end of course, with timing changes I performed, she was running like a champ on 87E10, and bonus is that she was now using way less fuel on the hiway. My brother paid me for every hour I put into that thing and left me a nice tip as well. I loved that guy(RIP) . If you have one of those Holleys, and it runs well, Thank the Good Lord. If not, put a 4bbl on it and call it done.