Highest vacuum or highest rpm is not always the best setting for idle mixture, you want the engine as smooth as possible, meaning you want it steady as far as rocking on the mounts. If you can't get it smooth then there's probably another reason such as a vacuum leak you haven't found or a weak cylinder. BTW there is no magic setting of mixture screws to get the best idle, the 1 1/2- 3 variances you see printed in books or magazines are just ball park settings to start from. Each carb and engine needs it's own particular setting, one size does not fit all. Many times when someone bottoms the mixture screws out the over tighten them and make a flat area on the taper of the screw causing the screws to be unresponsive to adjustments, you might want to remove the screws and inspect them.
Are you sure the balancer hasn't slipped on the hub and the timing isn't where it should be? If the car has power brakes the diaphragm could have a leak, pinching off the brake booster hose with a pair of needle nose pliers while running will confirm this one way or the other. I used to have a Snap On balance tester that would kill one cylinder at a time and it would tell you how many RPMs each would drop letting you zero in on a weak cylinder. The same thing can be accomplished with a tach and pulling one wire at a time and observing the amount of RPM drop.
The burning eyes from idling is lean or timing way off, or pre-ignition from a hot spot in a combustion chamber, something glowing such as carbon or a sharp edge. Filling a pop bottle with water and drizzling a small stream down the throat of the carb while running at about 1500-2000 RPM will remove carbon from the valves and piston tops and combustion chambers. Carbon can cause uneven compression, hot spots, hold a valve off it's seat. Running 16 ounces or so will many times smooth out an engine that you can't make idle correctly. Probably be some people scratching their heads on this one, I can tell you though it does work and I have smoothed the idle out and stopped pre-ignition on many many cars that no one else could make idle smooth. Done the way I've described it there are no problems, just don't drown the engine with water while doing it. You'll see the carbon come out the tailpipes behind the car.
You might also want to rev the engine and manually hold the choke fully closed while opening the throttle plates, opening the choke back up before it stalls and then rev it and repeat 2-3 times. If there is any small particles of dirt in the carb many times doing this will raise the vacuum in the circuits enough to dislodge it pull it through the circuit.
Some old time causes and cures for older cars that I learned during my years fixing them from the late 60s early 70s. Maybe one of these might apply to your case or not, the other things already suggested are just as valid, just some other things to check.
Good luck finding your problem............
