DD 6-71TI Stalls when Shifting Transmission

My port engine has developed a nasty habit of stalling when shifting the transmission. Occurs the worst possible times - like when maneuvering into a slip with a large group of onlookers.

What's puzzling is that it only happens after a long run and the engines are hot. Idle is set at 550 rpm and engine temp runs 165-175F. My temporary work around is to bump idle speed to 700 before shifting. It works, but I don't like the "thunk" as it drops into gear.

Dock chatter suggested maybe a line has fouled the prop (No, Checked an found prop & shaft clear), a miscalibrated tach, (I doubt it since it only happens when hot); or a fouled fuel cooler returning hot, low energy fuel to the tank (???)

Any suggestions?

.... this kind of thing is USUALLY found in the tune, or there is a slight binding in the rack.

The latter is VERY BAD and needs immediate attention, as it can lead to a runaway if it binds up on you completely. The former is usually a matter of where the buffer screw is, but you have to go through the entire tune-up procedure to get this right, so don't try to cheat and play with the buffer screw without checking everything else.