Just a thought. Are you sure you do not have a primer leak that is letting your fuel pump inject extra fuel into your engine through the primer ports on the cylinders that have them. Crack a primer line and, with the electric pump running, nothing should leak with the primer locked.
Chuck Ross RV4

This is correct...

8213C...take a look at this DOC, it will give you some insight on operation of your carb. The adjustments that are done are only for idle, and idle mixture. Above about 1400 RPM idle fuel metering isn't delivering fuel and it's all controlled with mixture knob. This is assuming the mixture cable is installed correct and gives full control stop-to-stop on the carb.

The carb is a red-herring...highly unlikely it's causing high EGT on just #3.

This is what I would do now in the order from easy to hard, which means from cheapest to expensive.

1. Swap EGT probes to see if the indication follows the swap, and determine if the probe is bad
2. Compression check and borescope to check exhaust valve operation
3. Check and test for induction leaks

One of the symptoms of an induction leak is no RPM rise when mixture is moved to idle cut-off. The fact that your mechanic enriched your idle mixture initially and you still couldn't get an RPM rise at cutoff points to this possibility. The fact that EGT is much higher on #3 than any other jug, and peaks much sooner when leaning, points to the leak being on #3. Is there a primer on #3? Check for leaks and cracks there, in addition to the intake pipe and fittings. Look for fuel staining...even mogas will leave some brownish/amber staining.

Cross beat me to it, but the idea is a little different. If you have a leak in the primer system that leak can suck in air when not priming, which will cause a leaner mixture on just that cylinder.