Turns out that this furnace was on an ongoing recall list for a possible overheat condition of the heat ex-changer, leading to property damage or worse. Here's the affected furnace models and website for more information:
The Coleman®, Coleman® Evcon, and Red T furnaces are used in manufactured housing. On these furnaces the name plate is found mounted on the left inside surface behind the lower panel. The furnaces are a silver color with white access panels.
These model numbers, and additional information, are found at this website address: http://dgatprogram.com
The Recall Program Support Center: (888) 665-4640.
Contractor came out to handle the Recall service.
This pic is not the actual furnace, but is a match.
First thing he did was to attempt starting the furnace. After he watched it shut down a few times, he checked manifold pressure - was 3.6 (spec on the gas valve was 3.5, natural gas). He checked flame sensor and agreed it was good. After finding no other obvious problems, he went ahead with the heat ex-changer replacement and said he would check the shutting down problem some more after finishing the recall work.
I watched the entire removal/replacement process, and there was no blockage around the baffle in the upper part of the heat ex-changer, nor in the stack above it going to the roof jack. After completing the replacement, he turns the furnace on and it was like it never had a problem to begin with!
When this contractor was attempting to start the furnace, before beginning the recall work, it was acting differently than it had been with my attempts, which were flame on, then shut down 5 seconds later. When he did it, the flame was coming on, but so was the blower, almost immediately. The flame would shut off in about 5 seconds, but the blower would keep on running. It was different with him, because he had the Fresh Air switch On, and my attempts were with that switch turned Off. During my initial attempts on my first day out there, I also tried it with the Fresh Air switch On, and got the same results as the contractor did, but all my subsequent attempts were with that switch turned Off.
For other non-pro's like myself, this furnace is a Coleman Evcon, Standard Blend Air II (there is also a more complex Deluxe Blend Air II furnace). Contractor was not familiar with it - I did some google-ing. This Standard model furnace has only a roof vent with a flex duct leading down to the furnace closet where it terminates at the upper left corner of the closet compartment, with an adjustable damper at its end, controlled by a motor (the Deluxe model has an attic fan and a couple of control boards, plus more switches in the furnace closet).
So, for this Standard model in question now... when the blower is on, this damper is opened to introduce fresh air into the home. The front panels of the furnace are vented (with filters) and the blower draws the fresh air into the cabinet and over the heat ex-changer and out to the floor vents (this is a mobile home). I've described this system, in case it's possible that this Fresh Air component could have anything to do with the flame shutting off prematurely. In retrospect, maybe I should have temporarily disconnected this Fresh Air component from the thermostat, or wherever it's connected to, to see if it was the problem.
The front of this furnace was very dusty, including the top surface of the control board, which was mounted horizontally in the box (labeled "A" in the picture). Neither the contractor nor I, ever did clean it (he didn't get a chance to - furnace starting working after his recall work). All I did was to remove and re-attach the two multi-pin connectors on the board in case they were not making good contact. I had also removed and re-connected connections at the Combustion Air motor, and switch or whatever that thing below the motor is called. Maybe that component proves induction air after achieving certain RPM speed of the motor (read about that somewhere)? I had also separated and reconnected the connector on top of the rectangular box ("A", in the pic).
If all the dust wasn't a factor, maybe the flame sensor circuit had a better ground after all the dis-assembly and re-assembly of the furnace walls, during the heat ex-changer replacement?