411A,
That's almost but not entirely accurate. I flew one of those old 4 engine piston transports (Wright R3350 turbo compounds), albeit a military one for which range was more important than schedule.
In that case, the optimum approach was to reduce RPM (with max BMEP) to cruise at the best range cruise speed for the weight. This meant that the last portion of the flight would be flown at some 15% slower than the initial cruise. (Made for a long night: I once flew a 20 hr flight, returning to Nova Scotia while retaining Jacksonville FLA as my alternate. Very glad wx above minima on arrival.)
For fast cruise, which commercial airliners used as you said,(unless on the hairy edge of range), indeed the TAS would increase by as much as 7-9% at max cruise power.
Was much more comfortable when I could get back to jets which have essentially no range penalty to fly at high cruise speed when at high flight levels.
Your coffin corner situation appears to have been found by a Pinnacle crew.