Your "tech" needs to put a digital manometer on the vent system and see what vacuum the pressure switch is seeing. That very simple move will tell him if there is a problem with the vent/intake/drain or not. Without doing this, he will not be able to diagnose the issue. Of course my guess is he doesn't have a digital manometer and know how to use it or he would have done this already.
What happens if you disconnect the intake pipe at the furnace and run with just the exhaust? You appear to be right on the line of needing 3" so it is possible that they cut it too close. Are the elbows used very long sweep or fairly sharp bends?
One other thought, be sure furnace is very level or leaning foward. If leaning backwards any, that could explain it.