Dealing with hesitation, not normally in 1st or 2nd gear, 99% of time in 3rd, 4th and 5th. Began in 4th & 5th after transmission replaced and plugs. Got worse, even after another set of plugs, wires, fuel filter and pump, converter, muffler, two coils, three complete diagnostics eventually averaging 140-180 compression #3 & 4 strongest. Scoping valves for valve bend burn or broken springs or others problems, leak down under 2-10%, fuel flow & pressure tests fine, amf sensor cleaned, but giving computer a high elevation read, fuel mix rich at 2000 rpm's with slight load. Strong in first and second gear. Starts sputtering into 3rd & 4th. Acts like it is flooding out, by creating similar load as slower speed in 1st & 2nd by riding brakes till sputtering begins, and a strong smell of unburned fuel.

Everything else checks out mechanically sound including transmission which is standard 5 speed. 145,000 miles on chassis, no leaks, no blue smoke or oil loss. Well taken care of.

One of three diagnostics showed Timing belt off or stretched by 6% and crank shaft pulley hub maybe 1% or 1/16" play.

Just did a new pulley hub and timing belt, Also put a new egr valve in.

Big question... what next?

...Computer next? Another sensor? Knock sensor? Fuel injectors even with normal fuel flow tests? What else? O2 sensor?

 

Sounds like you've got a misfire. The doesn't mean bad plugs, could be bad (stuck or dirty) injectors or even the coil pack starting to go.

start simple, it looks like you've jumped to serious conclusions without checking the three basic things needed to run: Fuel, Air, Spark.

 

Does engine run better cold?

Or does engine temp not matter?

Warm up engine then disconnect the EGR valve's vacuum hose and plug it, the hose.

Then test drive it, could be EGR valve is opening too soon and too much.

Unburnt fuel smell doesn't necessarily mean "rich" injector issue, mis-fire would mean unburnt fuel.

One thing that won't turn on the CEL(check engine light) but will cause limited RPMs and upper RPM mis-fires is a partially blocked exhaust system.

Vacuum gauges are not expensive and can help diagnose many issues on any engine, including valve train and timing, piston ring condition and clogged exhaust.
Good read here on using vacuum gauge: Technical Articles: Engine testing with a Vacuum Gauge - at Greg's Engine & Machine